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searching for Affine variety 20 found (106 total)

Observable subgroup (112 words) [view diff] exact match in snippet view article find links to article

observable subgroup of G if and only if the quotient variety G/K is a quasi-affine variety. Some basic facts about observable subgroups: Every normal algebraic

Locally nilpotent derivation (4,374 words) [view diff] exact match in snippet view article find links to article

{\displaystyle (k,+)} to the affine variety X = Spec ⁡ ( A ) {\displaystyle X=\operatorname {Spec} (A)} . Roughly speaking, an affine variety admitting "plenty"

Bernstein–Sato polynomial (1,562 words) [view diff] exact match in snippet view article find links to article

presented algorithms to compute the Bernstein–Sato polynomial of an affine variety together with an implementation in the computer algebra system SINGULAR

Vojta's conjecture (611 words) [view diff] exact match in snippet view article find links to article

crossings divisor, then the S {\displaystyle S} -integral points on the affine variety X ∖ D {\displaystyle X\setminus D} are not Zariski dense. For abelian

Formal holomorphic function (203 words) [view diff] exact match in snippet view article find links to article

sheaf of a related formal scheme. If V is an affine subvariety of the affine variety W defined by an ideal I of the coordinate ring R of W, then a formal

Toric variety (1,310 words) [view diff] exact match in snippet view article find links to article

taking the Zariski closure of the image of such a map, one obtains an affine variety. If the collection of lattice points A generates the character lattice

Galois connection (4,173 words) [view diff] exact match in snippet view article find links to article

affine variety Spec(R). More generally, there is an antitone Galois connection between ideals in the ring and subschemes of the corresponding affine variety

Derived scheme (2,280 words) [view diff] exact match in snippet view article find links to article

topological properties of affine varieties. For example, consider a smooth affine variety M ⊂ A n {\displaystyle M\subset \mathbb {A} ^{n}} . If we take a regular

Generic matrix ring (629 words) [view diff] exact match in snippet view article find links to article

generic matrix ring of size n is the coordinate ring of a noncommutative affine variety whose points are the Spec's of matrix rings of size n (see below for

Transcendental extension (1,680 words) [view diff] exact match in snippet view article find links to article

and this defines the dimension of X. It follows that, if X is not an affine variety, its dimension (defined as the transcendence degree of its function

Locally closed subset (836 words) [view diff] exact match in snippet view article find links to article

the closure of Y in X. (See also quasi-projective variety and quasi-affine variety.) Finite intersections and the pre-image under a continuous map of locally

Numerical algebraic geometry (1,283 words) [view diff] exact match in snippet view article find links to article

structure used to describe algebraic varieties. The witness set for an affine variety that is equidimensional consists of three pieces of information. The

Representation on coordinate rings (672 words) [view diff] exact match in snippet view article find links to article

of the orbit G ⋅ v λ {\displaystyle G\cdot v_{\lambda }} . It is an affine variety called the highest weight vector variety by Vinberg–Popov. It is multiplicity-free

Gröbner basis (9,909 words) [view diff] exact match in snippet view article find links to article

decoding methods were developed for correcting errors of cyclic codes, affine variety codes, algebraic-geometric codes and even general linear block codes

Projective space (5,656 words) [view diff] exact match in snippet view article find links to article

coordinates are common zeros of a set of homogeneous polynomials. Any affine variety can be completed, in a unique way, into a projective variety by adding

Semi-invariant of a quiver (1,435 words) [view diff] exact match in snippet view article find links to article

_{k}(k^{\mathbf {d} (s(\alpha ))},k^{\mathbf {d} (t(\alpha ))})} Such affine variety is endowed with an action of the algebraic group GL(d) := Πi∈ Q0 GL(d(i))

Valuation ring (3,695 words) [view diff] exact match in snippet view article find links to article

(p)\cap A} is called the center of p in A. For the function field on an affine variety X {\displaystyle X} there are valuations which are not associated to

Linear algebraic group (6,000 words) [view diff] exact match in snippet view article find links to article

algebraic variety. Various complications arise. For example, if X is an affine variety, then one can try to construct X/G as Spec of the ring of invariants

Algebraic torus (3,965 words) [view diff] exact match in snippet view article find links to article

E^{\times }} . To define it properly as an algebraic group one can take the affine variety defined by the equation x y = 1 {\displaystyle xy=1} in the affine plane

Space (mathematics) (9,311 words) [view diff] exact match in snippet view article

complement of the zero set of a linear polynomial is an affine space, and an affine variety was the intersection of a projective variety with an affine space. André