Derived categories of (nested) Hilbert schemes

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.

arXiv comment20 pages, added reference to result in new version of Jiang--Leung preprint

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Cited by in corpus (6)

• On the Chow theory of projectivizations
• Decompositions of moduli spaces of vector bundles and graph potentials
• On nonexistence of semi-orthogonal decompositions in algebraic geometry
• Paracanonical base locus, Albanese morphism, and semi-orthogonal indecomposability of derived categories
• Vector fields and admissible embeddings for quiver moduli
• Smooth components on special iterated Hilbert schemes