Details
| Original language | English |
|---|---|
| Article number | 28 |
| Journal | Selecta Mathematica, New Series |
| Volume | 28 |
| Issue number | 2 |
| Publication status | Published - 30 Dec 2021 |
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.
Keywords
- Autoequivalences, Derived categories, Fourier–Mukai transforms, Hilbert schemes of points, Kummer varieties
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Selecta Mathematica, New Series, Vol. 28, No. 2, 28, 30.12.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Universal functors on symmetric quotient stacks of Abelian varieties
AU - Krug, Andreas
AU - Meachan, Ciaran
N1 - Funding Information: We are very grateful to the anonymous referee of [36] for generously suggesting that the P-functor associated to the generalised Kummer could be extended to one on the Hilbert scheme of points and thus inspiring this work. We also thank the referee of the present paper for many helpful suggestions. Furthermore, we thank Gwyn Bellamy and Joe Karmazyn for helpful comments as well as Sönke Rollenske and Michael Wemyss for their invaluable guidance and support.
PY - 2021/12/30
Y1 - 2021/12/30
N2 - 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.
AB - 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.
KW - Autoequivalences
KW - Derived categories
KW - Fourier–Mukai transforms
KW - Hilbert schemes of points
KW - Kummer varieties
UR - http://www.scopus.com/inward/record.url?scp=85122092189&partnerID=8YFLogxK
U2 - 10.1007/s00029-021-00740-4
DO - 10.1007/s00029-021-00740-4
M3 - Article
AN - SCOPUS:85122092189
VL - 28
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
SN - 1022-1824
IS - 2
M1 - 28
ER -