Displaying similar documents to “The non-criticality of certain families of affine varieties.”

A characterization of proper regular mappings

T. Krasiński, S. Spodzieja (2001)

Annales Polonici Mathematici

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Let X, Y be complex affine varieties and f:X → Y a regular mapping. We prove that if dim X ≥ 2 and f is closed in the Zariski topology then f is proper in the classical topology.

Generalized polar varieties and an efficient real elimination

Bernd Bank, Marc Giusti, Joos Heintz, Luis M. Pardo (2004)

Kybernetika

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Let W be a closed algebraic subvariety of the n -dimensional projective space over the complex or real numbers and suppose that W is non-empty and equidimensional. In this paper we generalize the classic notion of polar variety of W associated with a given linear subvariety of the ambient space of W . As particular instances of this new notion of generalized polar variety we reobtain the classic ones and two new types of polar varieties, called dual and (in case that W is affine) conic....

On existence of double coset varieties

Artem Anisimov (2012)

Colloquium Mathematicae

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Let G be a complex affine algebraic group and H,F ⊂ G be closed subgroups. The homogeneous space G/H can be equipped with the structure of a smooth quasiprojective variety. The situation is different for double coset varieties F∖∖G//H. We give examples showing that the variety F∖∖G//H does not necessarily exist. We also address the question of existence of F∖∖G//H in the category of constructible spaces and show that under sufficiently general assumptions F∖∖G//H does exist as a constructible...

Non-uniruledness and the cancellation problem

Robert Dryło (2005)

Annales Polonici Mathematici

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Using the notion of uniruledness we indicate a class of algebraic varieties which have a stronger version of the cancellation property. Moreover, we give an affirmative solution to the stable equivalence problem for non-uniruled hypersurfaces.