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 of -points over special kinds of a fibered surface of Picard rank .
"Bayer–Macrì decomposition on Bridgeland moduli spaces over surfaces." Kyoto J. Math. 58 (3) 595 - 621, September 2018. https://doi.org/10.1215/21562261-2017-0031