Determinant, Wall Monodromy and Spherical Functor
<p>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 constru...
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2015
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| Online Access: | http://hdl.handle.net/10161/11378 |
| Summary: | <p>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.</p> === Dissertation |
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