Details
| Original language | English |
|---|---|
| Pages (from-to) | 167-187 |
| Number of pages | 21 |
| Journal | Michigan mathematical journal |
| Volume | 74 |
| Issue number | 1 |
| Publication status | Published - Feb 2024 |
Abstract
In this paper, we provide several results regarding the structure of derived categories of (nested) Hilbert schemes of points. We show that the criteria of Krug–Sosna and Addington for the universal ideal sheaf functor to be fully faithful resp. a P-functor are sharp. Then we show how to embed multiple copies of the derived category of the surface using these fully faithful functors. We also give a semiorthogonal decomposition for the nested Hilbert scheme of points on a surface, and finally we give an alternative proof of a semiorthogonal decomposition due to Toda for the symmetric product of a curve.
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In: Michigan mathematical journal, Vol. 74, No. 1, 02.2024, p. 167-187.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Derived Categories of (Nested) Hilbert Schemes
AU - Belmans, Pieter
AU - Krug, Andreas
N1 - Funding Information: The first author was supported by the Max Planck Institute for Mathematics and the University of Bonn. The second author was supported by the University of Marburg.
PY - 2024/2
Y1 - 2024/2
N2 - In this paper, we provide several results regarding the structure of derived categories of (nested) Hilbert schemes of points. We show that the criteria of Krug–Sosna and Addington for the universal ideal sheaf functor to be fully faithful resp. a P-functor are sharp. Then we show how to embed multiple copies of the derived category of the surface using these fully faithful functors. We also give a semiorthogonal decomposition for the nested Hilbert scheme of points on a surface, and finally we give an alternative proof of a semiorthogonal decomposition due to Toda for the symmetric product of a curve.
AB - In this paper, we provide several results regarding the structure of derived categories of (nested) Hilbert schemes of points. We show that the criteria of Krug–Sosna and Addington for the universal ideal sheaf functor to be fully faithful resp. a P-functor are sharp. Then we show how to embed multiple copies of the derived category of the surface using these fully faithful functors. We also give a semiorthogonal decomposition for the nested Hilbert scheme of points on a surface, and finally we give an alternative proof of a semiorthogonal decomposition due to Toda for the symmetric product of a curve.
UR - http://www.scopus.com/inward/record.url?scp=85187107595&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1909.04321
DO - 10.48550/arXiv.1909.04321
M3 - Article
AN - SCOPUS:85187107595
VL - 74
SP - 167
EP - 187
JO - Michigan mathematical journal
JF - Michigan mathematical journal
SN - 0026-2285
IS - 1
ER -