proper morphism
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Proper morphism — In algebraic geometry, a proper morphism between schemes is an analogue of a proper map between topological spaces. Contents 1 Definition 2 Examples 3 Properties and characterizations of proper morphisms … Wikipedia
Proper — may refer to:* Proper (liturgy), the part of a Christian liturgy that is specific to the date within the Liturgical Year * Proper frame, such system of reference in which object is stationary (non moving), sometimes also called a co moving frame… … Wikipedia
Proper map — In mathematics, a continuous function between topological spaces is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a proper morphism. Definition A function f : X rarr; Y… … Wikipedia
Quasi-finite morphism — In algebraic geometry, a branch of mathematics, a morphism f : X rarr; Y of schemes is quasi finite if it satisfies the following two conditions:* f is locally of finite type. * For every point y isin; Y , the scheme theoretic fiber X times; Y k… … Wikipedia
Finite morphism — In algebraic geometry, a branch of mathematics, a morphism of schemes is a finite morphism, if Y has an open cover by affine schemes Vi = SpecBi such that for each i, f − 1(Vi) = Ui is an open affine subscheme SpecAi, and the restriction of … 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
Coherent duality — In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the local… … Wikipedia
Étale cohomology — In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil… … Wikipedia
Coherent sheaf — In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a specific class of sheaves having particularly manageable properties closely linked to the geometrical properties of the underlying space … Wikipedia
Grothendieck–Hirzebruch–Riemann–Roch theorem — In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far reaching result on coherent cohomology. It is a generalisation of the Hirzebruch–Riemann–Roch theorem, about complex manifolds, which is itself a… … Wikipedia
Complete algebraic variety — In mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the projection morphism X × Y → Y is a closed map, i.e. maps closed sets onto closed sets.[1] The most common … Wikipedia
