Derived Categories of (Nested) Hilbert Schemes

authored by

Pieter Belmans, Andreas Krug

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.

Organisation(s)

Institute of Algebraic Geometry

External Organisation(s)

University of Luxembourg

Type

Article

Journal

Michigan mathematical journal

Volume

74

Pages

167-187

No. of pages

21

ISSN

0026-2285

Publication date

02.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all)

Electronic version(s)

https://doi.org/10.48550/arXiv.1909.04321 (Access: Open)
https://doi.org/10.1307/mmj/20216092 (Access: Closed)