Determinant, Wall Monodromy and Spherical Functor

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Date

2015

Authors

Wang, Kangkang

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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.

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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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