Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorization of generalized Theta functions revisited   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 ${\rm
dim}\,H^0(\sU_C,\Theta_{\sU_C})$ 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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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: ao-sci
1
The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an