Wanmin Liu: Bayer-Macrì decomposition on Bridgeland moduli spaces over surfaces

We find a decomposition of the local Bayer-Macrì map for the nef line bundle theory on the Bridgeland moduli spaces over surfaces and obtain the image of the local Bayer-Macrì map in the Néron-Severi group of the moduli space. The geometric meaning of the decomposition is given. From the decomposition, we obtain a precise correspondence between Bridgeland walls and Mori walls. As an application, we solve a problem raised by Arcara, Bertram, Coskun, Huizenga (Adv. Math. {235}(2013), 580-626) on the Hilbert scheme of n-points over projective plane.

This is my PhD thesis work. The details are given in the preprint on arXiv: http://arxiv.org/abs/1501.06397

In the first part of the talk, I will briefly introduce the Bridgeland stability conditions and Bayer-Macrì's determinant line bundle theory on Bridgeland moduli spaces. In the second part, I will introduce the Bayer-Macrì decomposition and give some examples on the birational geometry of the moduli spaces.