Perverse coherent sheaves on blow-ups at codimension 2 loci

Abstract

Let $f:X\to Y$ be the blow-up of a smooth projective variety $Y$ along its codimension two smooth closed subvariety. In this paper, we show that the moduli space of stable sheaves on $X$ and $Y$ are connected by a sequence of flip-like diagrams. The result is a higher dimensional generalization of the result of Nakajima and Yoshioka, which is the case of $\dim Y=2$. As an application of our general result, we study the birational geometry of the Hilbert scheme of two points.

27 pages, minor changes

References in corpus (2)

• Perverse coherent sheaves on blow-up. III. Blow-up formula from wall-crossing
• Stability conditions and birational geometry of projective surfaces

Cited by in corpus (1)

• Birational geometry of moduli spaces of perverse coherent sheaves on blow-ups