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Determinant, Wall Monodromy and Spherical Functor

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Date
2015
Author
Wang, Kangkang
Advisors
Aspinwall, Paul
Miller, Ezra
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Abstract

We apply the definition of determinant in the compactified moduli space as a generalization of the discriminant. We study the relationship between the wall monodromy and the determinant in the GIT wall crossing. The wall monodromy is an EZ-spherical functor in the sense of Horja. By constructing a fibration structure on Z, we obtain a semi-orthogonal decomposition of the derived category of coherent sheaves of Z, hence decompose the EZ-spherical functor into a sequence of its subfunctors. We also show that the intersection multiplicity of the discriminant and the exponent of the discriminant in the determinant both have their correspondences in this decomposition.

Type
Dissertation
Department
Mathematics
Subject
Mathematics
Permalink
https://hdl.handle.net/10161/11378
Citation
Wang, Kangkang (2015). Determinant, Wall Monodromy and Spherical Functor. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/11378.
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