Bayer–Macrì decomposition on Bridgeland moduli spaces over surfaces

Abstract

We find a decomposition formula of the local Bayer–Macrì map for the nef line bundle theory on the Bridgeland moduli space over a surface. If there is a global Bayer–Macrì map, then such a decomposition gives a precise correspondence from Bridgeland walls to Mori walls. As an application, we compute the nef cone of the Hilbert scheme $S^{\left[n\right]}$ of $n$-points over special kinds of a fibered surface $S$ of Picard rank $2$.