Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mccme.ru/tg2007/talks/Rittatore.pdf Дата изменения: Tue Nov 27 17:56:01 2007 Дата индексирования: Tue Oct 2 12:08:28 2012 Кодировка: Поисковые слова: http astrokuban.info astrokuban

A. Rittatore Universidad de la Republica Montevideo, Uruguay alvaro@cmat.edu.uy

Self-dual pro jective toric varieties
Pro jective duality can be thought as a way of recovering a pro jective variety from the set of its tangent hyperplanes. Dual varieties are a generalization to algebraic geometry of the Legendre transform of classical mechanics, and appear in several branches of mathematics. Generically, if X P(V ) is a pro jective variety, then its dual X P(V ) has codimension 1; if this is not the case, we say that X is defective. A self-dual pro jective variety is a variety X that is isomorphic to its dual as embedded varieties. Ein has provided the list of all smooth pro jective self-dual varieties; such a list contains all the smooth hypersufaces and a few more cases. In this talk we will focus on the duality of pro jective toric varieties; the study of the dual of these varieties has deep connections with the study of the so-called A-discriminants (Gelfand, Kapranov, Zelevisnky). Let T be an algebraic torus and V a finite dimensional rational T -module. Let X P(V ) be the closure of a T -orbit in P(V ) -- a pro jective toric variety. We will classify in terms of the combinatorial data associated to such a variety, when X is self-dual. In this way, we provide a large family of self-dual pro jective varieties. This is a joint work with M. Bourel and A. Dickenstein.

1