Categorical blow-up formula for Hilbert schemes of points

2021/10/15 by Koseki, Naoki · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.08315

Abstract

Let S be a smooth projective surface, and S be its blow-up at a point. In this paper, we study the derived category of the Hilbert scheme of points on the blow-up S. We obtain a semi-orthogonal decomposition consisting of the derived categories of the Hilbert schemes on the original surface S, which recovers the blow-up formula for the Euler characteristics obtained by Göttsche and Nakajima-Yoshioka. The proof uses the Quot formula, which was conjectured by Jiang and recently proved by Toda.

Cited by

• Instantons on the Blown-up Surface and the Affine Vertex Algebra
• Abel maps for integral curves via a derived perspective

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• Hilbert schemes of a surface and Euler characteristics
• Invariants of nested Hilbert and Quot schemes on surfaces
• Hilbert schemes of points on surfaces
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