THESIS
2015
Abstract
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
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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.
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