| E 2.304
Vortrag: Graded tilting for gauged Landau-Ginzburg models and geometric applications
Abstract: I will describe results of a joint paper (arXiv:1907.10099v2) with Andrei Teleman, in which we develop a graded tilting theory for gauged Landau-Ginzburg models of regular sections in vector bundles over projective varieties.
Our main theoretical result identifies -under certain conditions- the bounded derived category of the zero locus Z(s) of such a section s with the graded singularity category of a non-commutative graded quotient algebra A/s.
Our geometric applications all come from homogeneous GLSM presentations, where A appears as a graded non-commutative resolution of a graded invariant ring.
I will illustrate this with the case of Fano schemes of linear subspaces in a general projective hypersurface. Finally I will show how to get a purely algebraic description of the derived category of such a Fano scheme in terms of the linear algebra data defining it.