Displaying similar documents to “Some basic facts in algebraic geometry on a non algebraically closed field”

Quotients of an affine variety by an action of a torus

Olga Chuvashova, Nikolay Pechenkin (2013)

Open Mathematics

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Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/C T and the toric Hilbert scheme H. We introduce a notion of the main component H 0 of H, which parameterizes general T-orbit closures in X and their flat limits. The main component U 0 of the universal family U over H is a preimage of H 0. We define an analogue of a universal family WX over the main component of X/C T. We show that the toric Chow morphism restricted on...

Rigid analytic spaces

Marius Van der Put (1975-1976)

Groupe de travail d'analyse ultramétrique

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The set of points at which a morphism of affine schemes is not finite

Zbigniew Jelonek, Marek Karaś (2002)

Colloquium Mathematicae

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Assume that X,Y are integral noetherian affine schemes. Let f:X → Y be a dominant, generically finite morphism of finite type. We show that the set of points at which the morphism f is not finite is either empty or a hypersurface. An example is given to show that this is no longer true in the non-noetherian case.

On the space of real algebraic morphisms

Riccardo Ghiloni (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this Note, we announce several results concerning basic properties of the spaces of morphisms between real algebraic varieties. Our results show a surprising intrinsic rigidity of Real Algebraic Geometry and illustrate the great distance which, in some sense, exists between this geometry and Real Nash one. Let us give an example of this rigidity. An affine real algebraic variety X is rigid if, for each affine irreducible real algebraic variety Z , the set of all nonconstant regular...