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Mittwoch, 27.11.2019 | 14.00 - 15.20 Uhr | E 2.304

Oberseminar Algebra und Algebraische Geometrie: Prof. Dr. Christian Okonek, Universität Zürich

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.

 

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