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arXiv · 1707.07431

Factorization of generalized Theta functions revisited

Xiaotao Sun
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Abstract

This survey is based on my lectures given in last a few years. As a reference, constructions of moduli spaces of parabolic sheaves and generalized parabolic sheaves are provided. By a refinement of the proof of vanishing theorem, we show, without using vanishing theorem, a new observation that ${\rm dim}\,H^0(\sU_C,Θ_{\sU_C})$ is independent of all of the choices for any smooth curves. The estimate of various codimension and computation of canonical line bundle of moduli space of generalized parabolic sheaves on a reducible curve are provided in Section 6, which is completely new.

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Xiaotao Sun. 2017-07-24. Factorization of generalized Theta functions revisited. https://doi.org/10.1142/s1005386717000025

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