Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 10680-10701 |
| Seitenumfang | 22 |
| Fachzeitschrift | International Mathematics Research Notices |
| Jahrgang | 2015 |
| Ausgabenummer | 20 |
| Publikationsstatus | Veröffentlicht - 28 Jan. 2015 |
| Extern publiziert | Ja |
Abstract
We show that, for every smooth projective surface X and every n≥ 2, the push-forward along the diagonal embedding gives a ℙn-1-functor into the Sn-equivariant derived category of Xn. Using the Bridgeland-King-Reid-Haiman equivalence, this yields a new autoequivalence of the derived category of the Hilbert scheme of n points on X. If the canonical bundle of X is trivial and n=2, this autoequivalence coincides with the known EZ-spherical twist induced by the boundary of the Hilbert scheme. We also find n4 orthogonal ℙn-1-objects on the generalized Kummer variety associated to an abelian surface. They generalize the 16 spherical objects on the Kummer surface given by the exceptional curves.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Allgemeine Mathematik
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in: International Mathematics Research Notices, Jahrgang 2015, Nr. 20, 28.01.2015, S. 10680-10701.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On derived autoequivalences of Hilbert schemes and generalized Kummer varieties
AU - Krug, Andreas
PY - 2015/1/28
Y1 - 2015/1/28
N2 - We show that, for every smooth projective surface X and every n≥ 2, the push-forward along the diagonal embedding gives a ℙn-1-functor into the Sn-equivariant derived category of Xn. Using the Bridgeland-King-Reid-Haiman equivalence, this yields a new autoequivalence of the derived category of the Hilbert scheme of n points on X. If the canonical bundle of X is trivial and n=2, this autoequivalence coincides with the known EZ-spherical twist induced by the boundary of the Hilbert scheme. We also find n4 orthogonal ℙn-1-objects on the generalized Kummer variety associated to an abelian surface. They generalize the 16 spherical objects on the Kummer surface given by the exceptional curves.
AB - We show that, for every smooth projective surface X and every n≥ 2, the push-forward along the diagonal embedding gives a ℙn-1-functor into the Sn-equivariant derived category of Xn. Using the Bridgeland-King-Reid-Haiman equivalence, this yields a new autoequivalence of the derived category of the Hilbert scheme of n points on X. If the canonical bundle of X is trivial and n=2, this autoequivalence coincides with the known EZ-spherical twist induced by the boundary of the Hilbert scheme. We also find n4 orthogonal ℙn-1-objects on the generalized Kummer variety associated to an abelian surface. They generalize the 16 spherical objects on the Kummer surface given by the exceptional curves.
UR - http://www.scopus.com/inward/record.url?scp=84948396887&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnv005
DO - 10.1093/imrn/rnv005
M3 - Article
AN - SCOPUS:84948396887
VL - 2015
SP - 10680
EP - 10701
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 20
ER -