Displaying similar documents to “ K -theory of affine toric varieties.”

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...

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 a linearity criterion for algebraic systems of divisors on a projective variety

Umberto Bartocci, Lucio Guerra (1987)

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

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In the present paper, it is established in any characteristic the validity of a classical theorem of Enriques', stating the linearity of any algebraic system of divisors on a projective variety, which has index 1 and whose generic element is irreducible, as soon as its dimension is at least 2.

Higher order duality and toric embeddings

Alicia Dickenstein, Sandra Di Rocco, Ragni Piene (2014)

Annales de l’institut Fourier

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The notion of higher order dual varieties of a projective variety, introduced by Piene in 1983, is a natural generalization of the classical notion of projective duality. In this paper we study higher order dual varieties of projective toric embeddings. We express the degree of the second dual variety of a 2-jet spanned embedding of a smooth toric threefold in geometric and combinatorial terms, and we classify those whose second dual variety has dimension less than expected. We also...

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...

On a linearity criterion for algebraic systems of divisors on a projective variety

Umberto Bartocci, Lucio Guerra (1987)

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

Similarity:

In the present paper, it is established in any characteristic the validity of a classical theorem of Enriques', stating the linearity of any algebraic system of divisors on a projective variety, which has index 1 and whose generic element is irreducible, as soon as its dimension is at least 2.