Universal functors on symmetric quotient stacks of Abelian varieties

Krug, A. and Meachan, C. (2022) Universal functors on symmetric quotient stacks of Abelian varieties. Selecta Mathematica - New Series, 28(2), 28. (doi: 10.1007/s00029-021-00740-4)

Abstract

We consider certain universal functors on symmetric quotient stacks of Abelian varieties. In dimension two, we discover a family of P-functors which induce new derived autoequivalences of Hilbert schemes of points on Abelian surfaces; a set of braid relations on a holomorphic symplectic sixfold; and a pair of spherical functors on the Hilbert square of an Abelian surface, whose twists are related to the well-known Horja twist. In dimension one, our universal functors are fully faithful, giving rise to a semiorthogonal decomposition for the symmetric quotient stack of an elliptic curve (which we compare to the one discovered by Polishchuk–Van den Bergh), and they lift to spherical functors on the canonical cover, inducing twists which descend to give new derived autoequivalences here as well.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Meachan, Dr Ciaran
• Authors: Krug, A., and Meachan, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Selecta Mathematica - New Series
• Publisher: Springer
• ISSN: 1022-1824
• ISSN (Online): 1420-9020
• Published Online: 30 December 2021
• Copyright Holders: Copyright © 2021 The Authors
• First Published: First published in Selecta Mathematica - New Series 28(2): 28
• Publisher Policy: Reproduced under a Creative Commons License