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searching for Complex dimension 84 found (107 total)

Hurwitz surface (645 words) [view diff] exact match in snippet view article find links to article

as Hurwitz curves, interpreting them as complex algebraic curves (complex dimension 1 = real dimension 2). The Fuchsian group of a Hurwitz surface is

Complex projective plane (527 words) [view diff] exact match in snippet view article find links to article

two-dimensional complex projective space. It is a complex manifold of complex dimension 2, described by three complex coordinates ( Z 1 , Z 2 , Z 3 ) ∈ C

Algebraic surface (973 words) [view diff] exact match in snippet view article find links to article

geometry over the field of complex numbers, an algebraic surface has complex dimension two (as a complex manifold, when it is non-singular) and so of dimension

Stein manifold (1,475 words) [view diff] exact match in snippet view article find links to article

algebraic geometry. Suppose X {\displaystyle X} is a complex manifold of complex dimension n {\displaystyle n} and let O ( X ) {\displaystyle {\mathcal {O}}(X)}

Bioctonion (474 words) [view diff] exact match in snippet view article find links to article

domain of dimension 27. The second exceptional symmetric domain (of complex dimension 16) lives in the space M 2 , 1 ( O C ) {\displaystyle M_{2,1}(O_{C})}

Complex dynamics (4,690 words) [view diff] exact match in snippet view article find links to article

equilibrium measure can be much more complicated, as one sees already in complex dimension 1 from pictures of Julia sets. A basic property of the equilibrium

Kähler manifold (4,739 words) [view diff] exact match in snippet view article find links to article

a Kähler manifold X {\displaystyle X} is a Hermitian manifold of complex dimension n {\displaystyle n} such that for every point p {\displaystyle p}

Lagrangian Grassmannian (713 words) [view diff] exact match in snippet view article find links to article

dimension 2n. It may be identified with the homogeneous space of complex dimension ⁠1/2⁠n(n + 1) Sp(n)/U(n), where Sp(n) is the compact symplectic group

Super Minkowski space (2,186 words) [view diff] exact match in snippet view article find links to article

the exterior algebra of some vector space, as described here. The complex dimension of S {\displaystyle S} is 2 m {\displaystyle 2^{m}} . If the signature

Calabi flow (318 words) [view diff] exact match in snippet view article find links to article

the Calabi flow was found by Piotr Chruściel in the case that M has complex dimension equal to one. Xiuxiong Chen and others have made a number of further

Conifold (865 words) [view diff] exact match in snippet view article find links to article

{CP} ^{4}} . The space C P 4 {\displaystyle \mathbb {CP} ^{4}} has complex dimension equal to four, and therefore the space defined by the quintic (degree

Linear complex structure (2,918 words) [view diff] exact match in snippet view article find links to article

of VJ. Note that if VJ has complex dimension n then both V+ and V− have complex dimension n while VC has complex dimension 2n. Abstractly, if one starts

Dianalytic manifold (113 words) [view diff] exact match in snippet view article find links to article

manifolds were introduced by Klein (1882), and dianalytic manifolds of 1 complex dimension are sometimes called Klein surfaces. Klein, Felix (1882), Ueber Riemann's

Klein surface (1,028 words) [view diff] exact match in snippet view article find links to article

In mathematics, a Klein surface is a dianalytic manifold of complex dimension 1. Klein surfaces may have a boundary and need not be orientable. Klein

Generalized complex structure (3,142 words) [view diff] no match in snippet view article find links to article

^{*},} which is of (complex) dimension n − dim ⁡ ( E ) . {\displaystyle n-\dim(\mathbf {E} ).} Thus the total (complex) dimension is n. Gualtieri has

Complex analysis (2,538 words) [view diff] exact match in snippet view article find links to article

There is also a very rich theory of complex analysis in more than one complex dimension in which the analytic properties such as power series expansion carry

Thom conjecture (346 words) [view diff] exact match in snippet view article find links to article

class. This would imply the previous result because algebraic curves (complex dimension 1, real dimension 2) are symplectic surfaces within the complex projective

Hodge theory (4,339 words) [view diff] exact match in snippet view article find links to article

then their wedge product is necessarily zero because C has only one complex dimension; consequently, the cup product of their cohomology classes is zero

Weil cohomology theory (878 words) [view diff] exact match in snippet view article find links to article

the dimension is clear from the fact that a (complex) manifold of complex dimension n has real dimension 2n, so these higher cohomology groups vanish

Topological string theory (2,687 words) [view diff] exact match in snippet view article find links to article

are not spheres vanish unless the complex dimension of the spacetime is three, and so spacetimes with complex dimension three are the most interesting.

Marie-Louise Michelsohn (569 words) [view diff] exact match in snippet view article find links to article

_{n-1{\text{ times}}})=0,} in which ω is the Kähler form and n is the complex dimension. Note that, even though it is reported in multiple sources that Michelsohn

Complex polygon (393 words) [view diff] exact match in snippet view article find links to article

dimension, which may be represented as an Argand diagram. So a single complex dimension comprises two spatial dimensions, but of different kinds - one real

Infinite-dimensional holomorphy (1,358 words) [view diff] exact match in snippet view article find links to article

step in extending the theory of holomorphic functions beyond one complex dimension is considering so-called vector-valued holomorphic functions, which

Linearization (1,446 words) [view diff] exact match in snippet view article find links to article

equation (L-function) Quasilinearization The linearization problem in complex dimension one dynamical systems at Scholarpedia Linearization. The Johns Hopkins

Hirzebruch–Riemann–Roch theorem (913 words) [view diff] exact match in snippet view article find links to article

}H^{i}(X,E)} of the dimensions as complex vector spaces, where n is the complex dimension of X. Hirzebruch's theorem states that χ(X, E) is computable in terms

Hilbert's twenty-first problem (1,191 words) [view diff] exact match in snippet view article find links to article

what 'Fuchsian' means). With work by Helmut Röhrl, the case in one complex dimension was again covered. Isomonodromic deformation Treibich Kohn, Armando

Kodaira vanishing theorem (846 words) [view diff] exact match in snippet view article find links to article

Kunihiko Kodaira's result is that if M is a compact Kähler manifold of complex dimension n, L any holomorphic line bundle on M that is positive, and KM is

Hermitian symmetric space (7,418 words) [view diff] exact match in snippet view article find links to article

{m}},J)} is a real vector space with a complex structure J, whose complex dimension is given in the table. Correspondingly, there is a graded Lie algebra

K3 surface (5,246 words) [view diff] exact match in snippet view article find links to article

Roughly speaking, the space of all complex analytic K3 surfaces has complex dimension 20, while the space of K3 surfaces with Picard number ρ {\displaystyle

Classification theorem (650 words) [view diff] exact match in snippet view article find links to article

classification – Mathematical classification of surfaces of algebraic surfaces (complex dimension two, real dimension four) Nielsen–Thurston classification – Characterizes

Function of several complex variables (17,717 words) [view diff] exact match in snippet view article find links to article

Every Stein manifold of (complex) dimension n has the homotopy type of an n-dimensional CW-Complex. In one complex dimension the Stein condition can be

Shing-Tung Yau (10,542 words) [view diff] exact match in snippet view article find links to article

Simon Donaldson showed that, over a nonsingular projective variety of complex dimension two, a holomorphic vector bundle admits a hermitian Yang–Mills connection

Complex differential form (1,413 words) [view diff] exact match in snippet view article find links to article

where Hodge theory applies. Suppose that M is a complex manifold of complex dimension n. Then there is a local coordinate system consisting of n complex-valued

Complexification (2,069 words) [view diff] exact match in snippet view article find links to article

corresponding basis for VC is given by { ei ⊗ 1 } over the field C. The complex dimension of VC is therefore equal to the real dimension of V: dim C ⁡ V C =

Pseudoconvexity (735 words) [view diff] exact match in snippet view article find links to article

definition we can actually find a C∞ exhaustion function. In one complex dimension, every open domain is pseudoconvex. The concept of pseudoconvexity

Hyperkähler manifold (1,650 words) [view diff] exact match in snippet view article find links to article

a simply connected compact holomorphically symplectic manifold of complex dimension 2 n {\displaystyle 2n} with H 2 , 0 ( M ) = 1 {\displaystyle H^{2

Preimage theorem (454 words) [view diff] exact match in snippet view article find links to article

{\displaystyle g^{-1}(y)} is a complex submanifold of X {\displaystyle X} of complex dimension n − m . {\displaystyle n-m.} Fiber (mathematics) – Set of all points

The Remaining Signs of Past Centuries (1,858 words) [view diff] exact match in snippet view article find links to article

singular plane. This is distinct from hybrid images which display more complex dimension. The illustrations in The Remaining Signs of Past Centuries additionally

Algebraic curve (7,993 words) [view diff] exact match in snippet view article find links to article

curve resides in n-dimensional complex projective space CPn. This has complex dimension n, but topological dimension, as a real manifold, 2n, and is compact

Riemann sphere (3,392 words) [view diff] exact match in snippet view article find links to article

complex manifold, called the Riemann sphere. As a complex manifold of 1 complex dimension (i.e. 2 real dimensions), this is also called a Riemann surface. Intuitively

Long line (topology) (1,906 words) [view diff] exact match in snippet view article

Rosenlicht gave an example of a non-paracompact complex manifold of complex dimension 2. Lexicographic order topology on the unit square List of topologies

Tell It Again – Songs of Sense & Nonsense (743 words) [view diff] exact match in snippet view article find links to article

signatures—such as 5/4 and 7/8—which added a unique and technically complex dimension to the recording process. Andrews referred to Moondog as a brilliant

Picard–Lefschetz theory (795 words) [view diff] exact match in snippet view article find links to article

fiber at x. Note that this is the middle homology since the fibre has complex dimension k, hence real dimension 2k. The monodromy action of π1(P1 – {x1,

Schottky group (1,224 words) [view diff] exact match in snippet view article find links to article

under Möbius transformations (Bers 1975). It is a complex manifold of complex dimension 3g−3. It contains classical Schottky space as the subset corresponding

ELSV formula (2,468 words) [view diff] no match in snippet view article find links to article

{\overline {\mathcal {M}}}_{g,n}} is a smooth Deligne–Mumford stack of (complex) dimension 3g − 3 + n. (Heuristically this behaves much like complex manifold

Symplectic group (3,109 words) [view diff] exact match in snippet view article find links to article

In these cases Sp(2n, F) is a real or complex Lie group of real or complex dimension n(2n + 1), respectively. These groups are connected but non-compact

Quantum logic (4,045 words) [view diff] exact match in snippet view article find links to article

is the lattice of closed subspaces of a separable Hilbert space of complex dimension at least 3. Then for any quantum probability measure P on Q there

Wirtinger inequality (2-forms) (981 words) [view diff] exact match in snippet view article

corresponding calibrated submanifolds are the complex submanifolds of complex dimension k. This says in particular that every complex submanifold of a Kähler

Oper (mathematics) (890 words) [view diff] no match in snippet view article

matrices. Since P 1 {\displaystyle \mathbb {P} ^{1}} has only one (complex) dimension, a one-form has only one component, and so an s l ( 2 , C ) {\displaystyle

Toric variety (2,261 words) [view diff] exact match in snippet view article find links to article

geometry, the classification of smooth complete toric varieties of complex dimension n {\displaystyle n} and with m {\displaystyle m} Cartier divisors

Twistor theory (4,205 words) [view diff] exact match in snippet view article find links to article

{\displaystyle 4k} also admit a twistor correspondence with a twistor space of complex dimension 2 k + 1 {\displaystyle 2k+1} . The nonlinear graviton construction

General linear group (3,929 words) [view diff] exact match in snippet view article find links to article

\operatorname {GL} (n,\mathbb {C} )} , is a complex Lie group of complex dimension n 2 {\displaystyle n^{2}} . As a real Lie group (through realification)

Affine manifold (982 words) [view diff] no match in snippet view article find links to article

{\displaystyle z\mapsto A\cdot z+c} where n {\displaystyle n} is the (complex) dimension of the manifold, c ∈ C n , {\displaystyle c\in \mathbb {C} ^{n},}

Marieme Helie Lucas (576 words) [view diff] exact match in snippet view article find links to article

anti-democratic. The debates around immigration in European countries adds a complex dimension to that debate, for Lucas: "Unfortunately, the European Left and Far-Left

Kodaira dimension (2,406 words) [view diff] no match in snippet view article find links to article

curves of genus 0 is a point, the space of curves of genus 1 has (complex) dimension 1, and the space of curves of genus g ≥ 2 has dimension 3g − 3. The

Kobayashi–Hitchin correspondence (4,434 words) [view diff] exact match in snippet view article find links to article

after providing a new proof of the Narasimhan–Seshadri theorem in complex dimension one, Donaldson proved existence for algebraic surfaces in 1985. The

Lefschetz hyperplane theorem (1,762 words) [view diff] exact match in snippet view article find links to article

Andreotti–Frankel theorem, which states that a complex affine variety of complex dimension n {\displaystyle n} (and thus real dimension 2 n {\displaystyle 2n}

Von Neumann algebra (5,917 words) [view diff] exact match in snippet view article find links to article

1/n, 2/n, 3/n, ..., ∞. The standard module has M-dimension 1 (and complex dimension n2.) Type I∞ The M-dimension can be any of 0, 1, 2, 3, ..., ∞. The

Hermitian Yang–Mills connection (1,048 words) [view diff] exact match in snippet view article find links to article

Yang–Mills equations that define instantons. In particular, when the complex dimension of the Kähler manifold X {\displaystyle X} is 2 {\displaystyle 2}

Hodge conjecture (3,014 words) [view diff] exact match in snippet view article find links to article

disprove the Hodge conjecture. Let X be a compact complex manifold of complex dimension n. Then X is an orientable smooth manifold of real dimension 2 n {\displaystyle

Holomorphic tangent bundle (1,456 words) [view diff] exact match in snippet view article find links to article

{\displaystyle M} . Given a complex manifold M {\displaystyle M} of complex dimension n {\displaystyle n} , its tangent bundle as a smooth vector bundle

Complex projective space (3,929 words) [view diff] exact match in snippet view article find links to article

transformations). Thus CPn carries the structure of a complex manifold of complex dimension n, and a fortiori the structure of a real differentiable manifold

Nilmanifold (1,538 words) [view diff] exact match in snippet view article find links to article

nilmanifolds are usually not homogeneous, as complex varieties. In complex dimension 2, the only complex nilmanifolds are a complex torus and a Kodaira

Atiyah–Singer index theorem (7,553 words) [view diff] no match in snippet view article find links to article

the Chern-Weil homomorphism). Take X to be a complex manifold of (complex) dimension n with a holomorphic vector bundle V. We let the vector bundles E

Duality (mathematics) (6,694 words) [view diff] no match in snippet view article

cohomology of the constant sheaf C) Hi(X) ⊗ H2n−i(X) → C, where n is the (complex) dimension of X. Poincaré duality can also be expressed as a relation of singular

Differentiable manifold (9,497 words) [view diff] no match in snippet view article find links to article

atlas. For this reason, one refers separately to the "real" and "complex" dimension of a topological space with a holomorphic atlas. A differentiable

Teichmüller space (4,998 words) [view diff] exact match in snippet view article find links to article

on X {\displaystyle X} . The space of those is a complex space of complex dimension 3 g − 3 {\displaystyle 3g-3} , and the image of Teichmüller space

John Smillie (mathematician) (867 words) [view diff] case mismatch in snippet view article

Eric; Smillie, John; Ueda, Tetsuo (2012). "Parabolic Bifurcations in Complex Dimension 2". arXiv:1208.2577 [math.DS]. Bainbridge, Matt; Smillie, John; Weiss

Hurwitz's theorem (composition algebras) (3,682 words) [view diff] exact match in snippet view article

The space on which the Vi's act can be complexified. It will have complex dimension N. It breaks up into some of complex irreducible representations of

4-manifold (3,662 words) [view diff] exact match in snippet view article find links to article

(1985). "Geometries and geometric structures in real dimension 4 and complex dimension 2". Geometry and Topology. Lecture Notes in Mathematics. Vol. 1167

Regular element of a Lie algebra (1,569 words) [view diff] exact match in snippet view article find links to article

{\displaystyle M} , and the centralizer is an algebraic torus of complex dimension n {\displaystyle n} (real dimension 2 n {\displaystyle 2n} ); since

Jesús Rafael Soto (2,691 words) [view diff] exact match in snippet view article find links to article

situations inside nature. To reveal this situations in all of its complex dimension was the impulse that has fed his plastic research. "When you enter

Kobayashi metric (2,246 words) [view diff] exact match in snippet view article find links to article

description of which complex manifolds are Kobayashi hyperbolic in complex dimension 1. The picture is less clear in higher dimensions. A central open

Stable principal bundle (1,338 words) [view diff] exact match in snippet view article find links to article

ω ) {\displaystyle (X,\omega )} be a compact Kähler manifold of complex dimension n {\displaystyle n} . Suppose P → X {\displaystyle P\to X} is a holomorphic

Grassmannian (8,402 words) [view diff] no match in snippet view article find links to article

particular, this shows that the Grassmannian is compact, and of (real or complex) dimension k(n − k). In the realm of algebraic geometry, the Grassmannian can

Thomas–Yau conjecture (1,919 words) [view diff] exact match in snippet view article find links to article

Calabi–Yau manifold ( X , ω , Ω ) {\displaystyle (X,\omega ,\Omega )} of complex dimension n {\displaystyle n} , which is in particular a real symplectic manifold

CR manifold (5,630 words) [view diff] exact match in snippet view article find links to article

= n − 2 dim ⁡ L , {\displaystyle k=n-2\dim L,} where dim L is the complex dimension. In case k = 1, the CR structure is said to be of hypersurface type

Geometry Festival (2,867 words) [view diff] exact match in snippet view article find links to article

(Princeton University) - Metric geometry of Calabi–Yau manifolds in complex dimension two "NSF Award Search: Award # 0072580 - Geometry Festival". NSF.

Complexification (Lie group) (7,216 words) [view diff] exact match in snippet view article

}} decomposing GC into a disjoint union of double cosets of B. The complex dimension of a double coset BσB is determined by the length of σ as an element

Complex hyperbolic space (2,077 words) [view diff] exact match in snippet view article find links to article

varies from -4 (for complex lines) to -1 (for totally real planes). In complex dimension 1, every real plane in the tangent space is a complex line: thus the

Representation theory of the Lorentz group (19,763 words) [view diff] exact match in snippet view article find links to article

should be thought of as a real Lie algebra of real dimension twice its complex dimension. Likewise, a real form may actually also be complex as is the case

Translation surface (4,595 words) [view diff] exact match in snippet view article find links to article

{\displaystyle {\mathcal {H}}(\alpha )} is naturally a complex orbifold of complex dimension 2 g + m − 1 {\displaystyle 2g+m-1} (note that H ( 0 ) {\displaystyle

K-stability (8,333 words) [view diff] exact match in snippet view article find links to article

that the Yau–Tian–Donaldson conjecture holds for toric varieties of complex dimension 2. For arbitrary polarised varieties it was proven by Stoppa, also

Fortran 95 language features (9,484 words) [view diff] no match in snippet view article find links to article

read without a specified format for input is INTEGER :: i REAL :: a COMPLEX, DIMENSION(2) :: field LOGICAL :: flag CHARACTER(LEN=12) :: title CHARACTER(LEN=4)