Autoequivalences of derived categories via geometric invariant theory

By Daniel Halpern-Leistner, Ian Shipman. 2013

64 citations recorded by the source corpus.

We study autoequivalences of the derived category of coherent sheaves of a variety arising from a variation of GIT quotient. We show that these automorphisms are spherical twists, and describe how they result from mutations of semiorthogonal decompositions. Beyond the GIT setting, we show that all spherical twist autoequivalences of a dg-category can be obtained from mutation in this manner. Motivated by a prediction from mirror symmetry, we refine the recent notion of "grade restriction rules" in equivariant derived categories. We produce additional derived autoequivalences of a GIT quotient and propose an interpretation in terms of monodromy of the quantum connection. We generalize this observation by proving a criterion under which a spherical twist autoequivalence factors into a composition of other spherical twists.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/49e2633b68baee71946449d264b954c068590012

Citations in the corpus

• Spherical DG-functors (2013, unknown): “tegories of algebraic varieties our results have been anticipated and made use of even as the paper was being written. The works which already apply the results of this paper include [Add11], [DW13], [HLS13], [BPP13], [DS13]. A previous attempt at this general treatment was made in [Ann07]. Conceptu”