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birational morphism

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  • 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

  • Flat morphism — In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., : fP : OY,f(P) → OX,P is a flat map …   Wikipedia

  • Blowing up — This article is about the mathematical concept of blowing up. For information about the physical/chemical process, see Explosion. For other uses of Blow up , see Blow up (disambiguation). Blowup of the affine plane. In mathematics, blowing up or… …   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

  • Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… …   Wikipedia

  • Zariski's main theorem — In algebraic geometry, a field in mathematics, Zariski s main theorem, or Zariski s connectedness theorem, is a theorem proved by harvs|txt=yes|last=Zariski|year1=1943|year2=1949 which implies that fibers over normal points of birational… …   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

  • Canonical bundle — In mathematics, the canonical bundle of a non singular algebraic variety V of dimension n is the line bundle which is the nth exterior power of the cotangent bundle Ω on V. Over the complex numbers, it is the determinant bundle of holomorphic n… …   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

  • 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

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