Vorträge in der Woche 19.06.2017 bis 25.06.2017

Dienstag, 20.06.2017: Cuspidal representations II

Polyxeni Spilioti

Donnerstag, 22.06.2017: Stringy invariants of minimal models of nondegenerate hypersurfaces

Victor Batyrev (Universität Tübingen)

We apply the Minimal Model Program to nondegenerate hypersurfaces in algebraic tori and explain how to compute the stringy invariants of their minimal models. These results will be applied to nondegenerate hypersurfaces whose minimal models are Calabi-Yau varieties. Our main motivation is the Mirror Symmetry for Calabi-Yau varieties. In particular, we show that the formula of Vafa for the orbifold Euler number of Calabi-Yau hypersurfaces in weighted projective spaces agree with the combinatorial formula for the stringy Euler number of its mirrors suggested by Vafa and Hori.

Freitag, 23.06.2017: On Terminal Fano Varieties with a Torus Action of Complexity One

Michele Nicolussi

In toric geometry, Fano varieties correspond to certain lattice polytopes, whose lattice points determine the type of singularities of the variety. In this spirit we approach the larger family of Fano varieties with a torus action of complexity one. We associate to any such variety the “anticanonical complex”, a polyhedral complex that detects the type of singularities. Moreover, we present the classification results obtained up to this point: we classified terminal Fano threefolds of complexity one that do not allow any divisorial contraction. Among those there are the terminal Fano threefolds of complexity one having Picard number one.The techniques developed in the classification process are also briefly discussed.