,Factorization of Generalized Theta Functions Revisited

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This survey is based on my lectures given in the last 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 theorems,we show,without using vanishing theorems,a new observation that dim H0(UC,OUC) is independent of all of the choices for any smooth curves.The estimate of various codimensions 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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