Seminari 25 settembre dei proff. Ciliberto e Moyano Fernandez

 Il 25 settembre pomeriggio si terranno due seminari, entrambi in aula Anile, il primo del Prof. CIliberto alle ore 15:30 dal titolo: "A rationality criterion for varieties and applications to Fano threefolds". Il secondo del Prof. Moyano Fernandez alle ore 16:30 circa dal titolo: "Score sheets and monoids"

Seguono gli abstracts.

A rationality criterion for varieties and applications to Fano threefolds:
In 1938 U. Morin, improving on earlier results by G. Fano (1918), stated a projective classification theorem for varieties of dimension n >= 3 whose general surface sections are rational. Although Morin's result is correct, his proof is wrong. In the first part of this talk I will explain how to fix Morin's argument by using ideas from Mori's theory already exploited by F. Campana and H. Flenner to attack a quite similar problem. This part is joint work with C. Fontanari. In the second part of the talk I will make some application to rationality of Fano threefolds.

Score sheets and monoids
The set M_n of ordered score sheets of a round-robin football tournament played between n teams together with the pointwise addition has the structure of an affine monoid.
We present the study of the most important invariants of this monoid, namely the Hilbert basis, the multiplicity, the Hilbert series and the Hilbert function, which has been done by using Normaliz. In addition, we introduce the submonoids R_n resp. C_n of M_n for which the order is preserved after the leader team is disqualified, resp. all principal submatrices preserve the given ordering. Surprisingly, C_n turns out to be Gorenstein for n>2. This is a joint project with Bogdan Ichim.