We find a decomposition formula of the local Bayer-Macrì map for the nef line bundle theory on the Bridgeland moduli space over surface and obtain the image of the local Bayer-Macrì map in its Néron-Severi group. The geometric meaning of the decomposition is given. Fix a base moduli space and assume that we can identify Néron-Severi groups of different birational models of the moduli space. We then have a global Bayer-Macrì map. By the decomposition formula, we obtain a precise correspondence between Bridgeland walls in stability manifold of the surface and Mori walls in pseudo-effective cone of divisors on the base moduli space. As one application, we solve a conjecture raised by Arcara, Bertram, Coskun, Huizenga (Adv. Math. 235(2013), 580-626) on the Hilbert scheme of p...[ Read more ]

We find a decomposition formula of the local Bayer-Macrì map for the nef line bundle theory on the Bridgeland moduli space over surface and obtain the image of the local Bayer-Macrì map in its Néron-Severi group. The geometric meaning of the decomposition is given. Fix a base moduli space and assume that we can identify Néron-Severi groups of different birational models of the moduli space. We then have a global Bayer-Macrì map. By the decomposition formula, we obtain a precise correspondence between Bridgeland walls in stability manifold of the surface and Mori walls in pseudo-effective cone of divisors on the base moduli space. As one application, we solve a conjecture raised by Arcara, Bertram, Coskun, Huizenga (Adv. Math. 235(2013), 580-626) on the Hilbert scheme of points over projective plane. As another application, we find the ample cone of Hilbert scheme of points over Hirzebruch surface or a special elliptic surface.