birational mapping

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• Birational geometry — In mathematics, birational geometry is a part of the subject of algebraic geometry, that deals with the geometry of an algebraic variety that is dependent only on its function field. In the case of dimension two, the birational geometry of… …   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

• Rational variety — In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to projective space of some dimension over K. This is a question on its function field: is it up to isomorphism the field of all… …   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

• Pluricanonical ring — In mathematics, the pluricanonical ring of an algebraic variety V (which is non singular), or of a complex manifold, is the graded ring R(V,K)=R(V,K V) of sections of powers of the canonical bundle K .Its n th graded component (for ngeq 0) is::R… …   Wikipedia

• Geometric genus — In algebraic geometry, the geometric genus is a basic birational invariant p g of algebraic varieties, defined for non singular complex projective varieties (and more generally for complex manifolds) as the Hodge number h n ,0 (equal to h 0, n by …   Wikipedia

• List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… …   Wikipedia

• Motive (algebraic geometry) — For other uses, see Motive (disambiguation). In algebraic geometry, a motive (or sometimes motif, following French usage) denotes some essential part of an algebraic variety . To date, pure motives have been defined, while conjectural mixed… …   Wikipedia

• Ample line bundle — In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold M into projective space. An ample line bundle is one such that some positive power is very ample. Globally… …   Wikipedia

• List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia

• Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia