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searching for Complex algebraic variety 22 found (34 total)

alternate case: complex algebraic variety

Complex dimension (408 words) [view diff] exact match in snippet view article find links to article

dimension usually refers to the dimension of a complex manifold or a complex algebraic variety. These are spaces in which the local neighborhoods of points (or

Hodge cycle (255 words) [view diff] exact match in snippet view article find links to article

Hodge class is a particular kind of homology class defined on a complex algebraic variety V, or more generally on a Kähler manifold. A homology class x

Higgs bundle (548 words) [view diff] exact match in snippet view article find links to article

category of flat holomorphic connections on a smooth projective complex algebraic variety, the category of representations of the fundamental group of the

Fake projective space (78 words) [view diff] exact match in snippet view article find links to article

In mathematics, a fake projective space is a complex algebraic variety that has the same Betti numbers as some projective space, but is not isomorphic

GKM variety (139 words) [view diff] exact match in snippet view article find links to article

In algebraic geometry, a GKM variety is a complex algebraic variety equipped with a torus action that meets certain conditions. The concept was introduced

Equisingularity (123 words) [view diff] exact match in snippet view article find links to article

different from the usual Whitney stratification on a real or complex algebraic variety. stratified space O. Zariski, Some open questions in the theory

Algebraic cycle (1,472 words) [view diff] exact match in snippet view article find links to article

Institute's Millennium Prize Problems, predicts that the topology of a complex algebraic variety forces the existence of certain algebraic cycles. The Tate conjecture

Hodge conjecture (3,049 words) [view diff] exact match in snippet view article find links to article

geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties. In simple terms, the Hodge conjecture asserts

Riemann's existence theorem (528 words) [view diff] exact match in snippet view article find links to article

which says that the category of finite topological coverings of a complex algebraic variety is equivalent to the category of finite étale coverings of the

Complex manifold (1,338 words) [view diff] exact match in snippet view article find links to article

orientable surface, modulo biholomorphic equivalence, itself forms a complex algebraic variety called a moduli space, the structure of which remains an area

Mordellic variety (278 words) [view diff] exact match in snippet view article find links to article

this is in turn equivalent to X being pseudo-canonical. For a complex algebraic variety X we similarly define the analytic special or exceptional set

Riemann–Hilbert correspondence (1,480 words) [view diff] exact match in snippet view article find links to article

cohomology and singular/Betti cohomology. Suppose that X is a smooth complex algebraic variety. Riemann–Hilbert correspondence (for regular singular connections):

Euler characteristic (3,531 words) [view diff] exact match in snippet view article find links to article

This applies in particular if M and N are subvarieties of a complex algebraic variety. In general, the inclusion–exclusion principle is false. A counterexample

Algebraic geometry and analytic geometry (2,782 words) [view diff] exact match in snippet view article find links to article

algebraic varieties. Let X {\displaystyle X} be a projective complex algebraic variety. Because X {\displaystyle X} is a complex variety, its set of

Calabi–Yau manifold (3,303 words) [view diff] exact match in snippet view article find links to article

surfaces in P 3 {\displaystyle \mathbb {P} ^{3}} , such as the complex algebraic variety defined by the vanishing locus of x 0 4 + x 1 4 + x 2 4 + x 3

Perverse sheaf (2,265 words) [view diff] exact match in snippet view article find links to article

Here jx is the inclusion map of the point x. If X is a smooth complex algebraic variety and everywhere of dimension d, then F [ d ] {\displaystyle {\mathcal

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

necessarily smooth or compact. Namely, the cohomology of any complex algebraic variety has a more general type of decomposition, a mixed Hodge structure

Mixed Hodge module (1,596 words) [view diff] exact match in snippet view article find links to article

the category of mixed Hodge modules actually provides. Given a complex algebraic variety X {\displaystyle X} there is an abelian category MHM ( X ) {\displaystyle

Borel–Moore homology (2,666 words) [view diff] exact match in snippet view article find links to article

oriented manifold M of dimension n (in particular, every smooth complex algebraic variety), not necessarily compact, has a fundamental class [ M ] ∈ H n

Sheaf cohomology (5,833 words) [view diff] exact match in snippet view article find links to article

Hj(X,E) and Hcj(X,E) are finitely generated. For example, any complex algebraic variety X, with its classical (Euclidean) topology, is compactifiable

Hodge structure (4,874 words) [view diff] exact match in snippet view article find links to article

common with the Hodge structure arising from X considered as a complex algebraic variety. Sergei Gelfand and Yuri Manin remarked around 1988 in their Methods

Poincaré lemma (5,640 words) [view diff] exact match in snippet view article find links to article

For example, if one considers algebraic differential forms on a complex algebraic variety (in the Zariski topology), the lemma is not true for those differential