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arXiv · 1909.04321

Derived categories of (nested) Hilbert schemes

Pieter Belmans·Andreas Krug
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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 $\mathbb{P}$-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 elementary proof of a semiorthogonal decomposition due to Toda for the symmetric product of a curve.

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Pieter Belmans, Andreas Krug. 2019-09-10. Derived categories of (nested) Hilbert schemes. https://doi.org/10.1307/mmj/20216092

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