Modul: MAT770 Oberseminar: Algebraische Geometrie

## The gauged Landau-Ginzburg model of a Beauville-Donagi hyper-Kähler 4-fold

Prof. Dr. Christian Okonek talk

**Date:** 10.12.18 **Time:** 13.15 - 14.45 **Room:** Y27H25

This is a progress report on a joint project with A. Teleman, whose goal is to describe the derived category of a Beauville-Donagi hyper-Kähler 4-fold. Let f be a general cubic form in 6 variables, Z(f) the associated projective cubic hypersurface. The Beauville-Donagi hyper-Kähler 4-fold of f is the Fano variety X(f) of lines in Z(f); it admits a description by a linear Landau-Ginzburg model. I will explain a conjectural equivalence of the bounded derived category D^b(X(f)) of X(f) with a purely algebraic category, the graded singularity category of a skew algebra associated with the Sebastiani-Thom polynomial f+f. Our approach uses derived factorization categories of the Landau-Ginzburg model of X(f) and C*-equivariant VGIT; it is motivated by a K-equivalence conjecture for certain Deligne-Mumford stacks.