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arXiv · 1710.08618

Universal functors on symmetric quotient stacks of Abelian varieties

Andreas Krug·Ciaran Meachan
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Abstract

We consider certain universal functors on symmetric quotient stacks of Abelian varieties. In dimension two, we discover a family of $\mathbb{P}$-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.

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Andreas Krug, Ciaran Meachan. 2017-10-24. Universal functors on symmetric quotient stacks of Abelian varieties. https://doi.org/10.1007/s00029-021-00740-4

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