Displaying 81 – 100 of 315

Showing per page

Generalized polar varieties and an efficient real elimination

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

Kybernetika

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. We show that...

Homological projective duality

Alexander Kuznetsov (2007)

Publications Mathématiques de l'IHÉS

We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections are...

Currently displaying 81 – 100 of 315