Birational invariant information

algebraic geometry, a birational invariant is a property that is preserved under birational equivalence. A birational invariant is a quantity or object...

In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside...

In algebraic geometry, the geometric genus is a basic birational invariant pg of algebraic varieties and complex manifolds. The geometric genus can be...

h2,0 was called the geometric genus pg. The third, h1,1, is not a birational invariant, because blowing up can add whole curves, with classes in H1,1. It...

canonical ring and therefore likewise the Kodaira dimension is a birational invariant: Any birational map between smooth compact complex manifolds induces an isomorphism...

smooth projective varieties over a field, the Brauer group is a birational invariant. It has been fruitful. For example, when X is also rationally connected...

not birational invariants. However, locating and classifying the singularities of a curve is one way of computing the genus, which is a birational invariant...

dimension of the underlying variety. Bigness is a birational invariant: If f : Y → X is a birational morphism of varieties, and if L is a big line bundle...

the G-invariant rational functions on it, as the function field of the quotient variety. Unfortunately this — the point of view of birational geometry...

global sections H0(X,KXd) has the remarkable property that it is a birational invariant of smooth projective varieties X. That is, this vector space is canonically...

2016-03-07. Voskresenskii, V. S. (1998). Algebraic groups and their birational invariants. Translations of mathematical monographs. American Math. Soc. Tits...

algebraic variety X {\displaystyle X} is a combinatorial invariant of importance to the birational geometry of X {\displaystyle X} . Let X {\displaystyle...

variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0, this was proved...

B\circ A} . The maps A {\displaystyle A} and B {\displaystyle B} are birational mappings of order 2, and have the following action. A ( x 1 , … , x 2...

interior of the cone of effective divisors. Bigness can be viewed as a birationally invariant analog of ampleness. For example, if f : X → Y {\displaystyle f\colon...

Among his main contributions to algebraic geometry are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His...

of given degree d from an algebraic curve to projective space Pn. In birational geometry, Noether introduced the fundamental technique of blowing up in...

Cremona transformation is a birational map from a projective space to itself cross-ratio The cross-ratio is an invariant of 4 points on a projective line...

ISBN 9780521802833. Voisin, Claire (2019). "Birational Invariants and Decomposition of the Diagonal". Birational Geometry of Hypersurfaces. Lecture Notes...

rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means...

\ldots ,x_{n}]/I} is called the homogeneous coordinate ring of X. Basic invariants of X such as the degree and the dimension can be read off the Hilbert...

algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety...