Personal webpage of Valentina Kiritchenko

Faculty of Mathematics

Wednesday, May 15, 17:00 and 18:30, room 306

shinymath, · Categories: Без рубрики

17:00 Boris Nazarov: Batyrev’s correspondence between lattice simplices and finite torus subgroups

This is an addendum to the preceding talk on the classification of small lattice polytopes.

All 16 reflexive polygons

17:30 Roman Krutovskiy: Gorenstein polytopes and toric Del Pezzo varieties

The material of this mini-talk is not necessary for understanding of the subsequent main talks. Its aim is to provide an algebraically geometric motivation for classification of all Gorenstein polytopes of degree two. I will briefly remind some general properties of toric varieties. Especially, I will give a description of the canonical class in terms of the underlying fan. Finally, I will formulate a theorem which establishes conditions on the underlying polytope of a projective toric variety X which guarantee that X is a Gorenstein Del Pezzo variety. Basic knowledge of toric varieties is expected.

18:30 Roman Krutovskiy, Grigory Yurgin: Сlassification of Gorenstein polytopes

The goal of our two joint talks is to obtain the classification of Gorenstein polytopes of degree two, which is equivalent to classifying all Gorenstein toric Del Pezzo varieties. On the first half (May 15, 18:30) we introduce the notion of a Gorenstein polytope and start our classification using methods of commutative algebra. On the second half (May 22, 18:30) we finish the classification using combinatorial approach and the results of the first half. The talks are independent form the preceding mini-talk (and do not require the knowledge of toric varieties). All necessary defenitions and facts from commutative algebra will be given during the talks.