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

fundamental theorems for the birational geometry of surfaces is Castelnuovo's theorem. This states that any birational map between algebraic surfaces...

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

a classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry. Enriques was born in Livorno, and brought...

Blowups are the most fundamental transformation in birational geometry, because every birational morphism between projective varieties is a blowup. The...

in the area of algebraic geometry and a professor at Princeton University. Xu is known for his work in birational geometry, the minimal model program...

algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model...

1965. Iitaka 1970. Iitaka 1971. J. A. Chen and M. Chen, Explicit birational geometry of 3-folds and 4-folds of general type III, Theorem 1.4. O. Fujino...

mathematics, the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry, particularly on algebraic surfaces, centered...

linear systems became a basic tool of birational geometry as practised by the Italian school of algebraic geometry. The technical demands became quite stringent;...

giving the fundamental Kleinian geometry on projective space, they concerned themselves also with the higher-degree birational transformations. This weaker...

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism...

modern birational geometry. In 2010 he received the Leverhulme Prize in mathematics and statistics for his contributions to algebraic geometry, and in...

dimension 3 flips are used to construct minimal models, and any two birationally equivalent minimal models are connected by a sequence of flops. It is...

Hilbert's sixteenth problem Cubic plane curve Hyperelliptic curve Birational geometry Conic section Elliptic curve Fractional ideal Function field of an...

In birational geometry, the Cremona group, named after Luigi Cremona, is the group of birational automorphisms of the n {\displaystyle n} -dimensional...

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

one of the most powerful formulas in algebraic geometry. An important tool of modern birational geometry is inversion of adjunction, which allows one to...

In mathematics, Lüroth's theorem asserts that every field that lies between a field K and the rational function field K(X) must be generated as an extension...

tremendously both from techniques in analysis and in pure birational geometry. Complex geometry has significant applications to theoretical physics, where...

Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive...

awarded his Ph.D. ("candidate degree") in 1976. Shokurov works on the birational geometry of algebraic varieties. After obtaining his Ph.D., he worked at the...

type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2; that is...

to the general n. Therefore The study of the higher-dimensional birational geometry decompose to the part of κ=-∞,0,n and the fiber space whose fibers...

tracing through the proof of the theorem it is possible to do so. Birational geometry Blowing up Function field of an algebraic variety Resolution of singularities...

refer to: Minimal model (birational geometry), classification of algebraic varieties with the goal to construct a birational model of any complex projective...

geometry can exhibit discontinuities of a kind that are detected by flatness. For instance, the operation of blowing down in the birational geometry of...

In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic...

In arithmetic geometry, the Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines whether a given set...

the 5-sphere, i.e. torsion. In birational geometry, a complex rational surface is any algebraic surface birationally equivalent to the complex projective...