Bridgeland wall-crossing for some Simpson moduli spaces on ${\mathbb{P}}^1\times {\mathbb{P}}^1$

Abstract

We investigate the wall-crossing behavior as Bridgeland moduli spaces for some Simpson moduli spaces of Gieseker-semistable torsion sheaves on ${\mathbb{P}}^1\times {\mathbb{P}}^1$ with linear Hilbert polynomial. In particular, we recover some of the birational transformations of these spaces described by Maican and Chung-Moon as wall-crossing maps in certain slices of $Stab({\mathbb{P}}^1\times {\mathbb{P}}^1)$.

18 pages, 3 figures, comments are welcome

References in corpus (1)

• On the geometry of the moduli space of sheaves supported on curves of genus two in a quadric surface