Examples of 'algebraic varieties' in a sentence
Meaning of "algebraic varieties"
algebraic varieties: Algebraic varieties are objects studied in algebraic geometry, a branch of mathematics that explores the relationships between algebraic equations and geometric shapes. These varieties are solution sets to systems of polynomial equations in several variables, which can be analyzed and classified based on their properties and geometric structures
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- plural of algebraic variety
How to use "algebraic varieties" in a sentence
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algebraic varieties
Consider on complex algebraic varieties in the following.
This approach is essential for classifying algebraic varieties.
Algebraic varieties are the central objects of study in algebraic geometry.
Smooth complex algebraic varieties.
A large part of singularity theory is devoted to the singularities of algebraic varieties.
Rationality of algebraic varieties.
Algebraic varieties differ widely in how many birational automorphisms they have.
Modern generalizations of algebraic varieties.
The coordinate rings of algebraic varieties are important examples of quotient rings in algebraic geometry.
On projections of real algebraic varieties.
GAGA theorems relate algebraic varieties over the complex numbers to the corresponding analytic spaces.
They form a wide class among notable algebraic varieties found in nature.
Schemes are likewise glued together from affine schemes, which are a generalization of algebraic varieties.
He is interested in the cohomology of algebraic varieties and the theory of motives.
We use a relation between left cosets and points on certain projective algebraic varieties.
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Fano varieties can be considered the algebraic varieties which are most similar to projective space.
Hypersurfaces have some specific properties that are not shared with other algebraic varieties.
Another example is given by " families " of algebraic varieties parametrised by another variety.
We formulate an analogue of the integral Hodge conjecture for real algebraic varieties.
In higher dimensions, moduli of algebraic varieties are more difficult to construct and study.
The terminology arises from the case of the Zariski topology of algebraic varieties.
Under this definition, non-irreducible algebraic varieties are called algebraic sets.
Additionally, he has made contributions to the deformation theory of algebraic varieties.
Abstract, The birational classification of algebraic varieties is a central problem in algebraic geometry.
The first part is about three-dimensional complex algebraic varieties.
Smooth complex algebraic varieties are complex manifolds, including: Complex vector spaces.
In another direction, toric varieties are algebraic varieties acted on by a torus.
Generalizations of this definition are possible, for instance, to complex manifolds and algebraic varieties.
Algebraic varieties and schemes Non-singular algebraic varieties over the real or complex numbers are manifolds.
In order to prove this, some birational invariants of algebraic varieties are needed.
Smooth complex algebraic varieties = = = Smooth complex algebraic varieties are complex manifolds, including, * Complex vector spaces.
In category theory, an algebraic group is a group object in the category of algebraic varieties.
Category: Algebraic varieties.
In algebraic geometry, the Zariski topology is a topology chosen for algebraic varieties.
Abstract, We consider certain cohomology groups with support for sheaves over algebraic varieties.
Examples of Stein manifolds include non-compact Riemann surfaces and non-singular affine complex algebraic varieties.
In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties.
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