birational equivalence

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• Birational invariant — In algebraic geometry, a birational invariant is a quantity or object that is well defined on a birational equivalence class of algebraic varieties. In other words, it depends only on the function field of the variety.For example in the case of… …   Wikipedia

• Minimal model (birational geometry) — In algebraic geometry, more specifically in the field of birational geometry, the theory of minimal models is part of the birational classification of algebraic varieties. Its goal is to construct, given a variety satisying certain restrictions,… …   Wikipedia

• Rational mapping — In mathematics, in particular the subfield of algebraic geometry, a rational map is a kind of partial function between algebraic varieties. In this article we use the convention that varieties are irreducible.DefinitionA first attemptSuppose we… …   Wikipedia

• Enriques–Kodaira classification — In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes. For each of these classes, the surfaces in the class can be parametrized by a moduli space. For most of the classes the moduli… …   Wikipedia

• Enriques-Kodaira classification — In mathematics, the Enriques Kodaira classification is a classification of compact complex surfaces. For complex projective surfaces it was done by Federigo Enriques, and Kunihiko Kodaira later extended it to non algebraic compact surfaces. It… …   Wikipedia

• Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …   Wikipedia

• Minimal model program — In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is as simple as possible. The subject has its… …   Wikipedia

• Montgomery curve — In mathematics the Montgomery curve is a form of elliptic curve, different from the usual representation (Weierstrass form). It has been introduced by Peter L.Montgomery in,[1] and it has been used since 1987 for certain computations, and in… …   Wikipedia

• Algebraic surface — In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface is therefore of complex dimension two (as a complex manifold, when it is non singular)… …   Wikipedia

• Federigo Enriques — (5 January 1871 –14 June 1946) was an Italian mathematician, now known principally as the first to give a classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry.He was born in Livorno, and… …   Wikipedia

• Resolution (mathematics) — In mathematics, a resolution may mean:* a resolution in homological algebra, i.e. injective resolution, or projective resolution/free resolution * resolution of singularities, a fundamental issue of birational geometry, whether a birational… …   Wikipedia