Categorical blow-up formula for Hilbert schemes of points

Abstract

Let $S$ be a smooth projective surface, and $\hat{S}$ 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 $\hat{S}$. 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.

13 pages, fixed an error in Theorem 5.4. I would like to thank Wu-yen Chuang for pointing out the error

References in corpus (3)

• Derived categories of Quot schemes of locally free quotients
• A Categorical Quantum Toroidal Action on Hilbert Schemes
• Derived categories of Quot schemes of locally free quotients via categorified Hall products

Cited by in corpus (1)

• Derived categories of Quot schemes of locally free quotients via categorified Hall products