Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Hodge theoretic projective structure on Riemann surfaces   Given any compact Riemann surface $C$, there is a canonical meromorphic
2--form $\widehat\eta$ on $C\times C$, with pole of order two on the diagonal
$\Delta\, \subset\, C\times C$, constructed in \cite{cfg}. This meromorphic
2--form $\widehat\eta$ produces a canonical projective structure on $C$. On the
other hand the uniformization theorem provides another canonical projective
structure on any compact Riemann surface $C$. We prove that these two
projective structures differ in general. This is done by comparing the
$(0,1)$--component of the differential of the corresponding sections of the
moduli space of projective structures over the moduli space of curves. The
$(0,1)$--component of the differential of the section corresponding to the
projective structure given by the uniformization theorem was computed by Zograf
and Takhtadzhyan in \cite{ZT} as the Weil--Petersson K\"ahler form
$\omega_{wp}$ on the moduli space of curves. We prove that the
$(0,1)$--component of the differential of the section of the moduli space of
projective structures corresponding to $\widehat{\eta}$ is the pullback of a
nonzero constant scalar multiple of the Siegel form, on the moduli space of
principally polarized abelian varieties, by the Torelli map.

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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph