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General expansion for period maps of Riemann surfaces

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Abstract

In this paper, we get the full expansion for period map from the moduli space \( \mathcal{M}_g \) of curves to the coarse moduli space \( \mathcal{A}_g \) of g-dimensional principally polarized abelian varieties in Bers coordinates. This generalizes fully the famous Rauch’s variational formula. As applications, we compute the curvature of Siegel metric at point [X] with Π([X]) = \( \sqrt { - 1} I_g \) and the Christoffel symbols of L 2-induced Bergman metric on \( \mathcal{M}_g \).

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  1. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    FangLiang Yin

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  1. FangLiang Yin
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Yin, F. General expansion for period maps of Riemann surfaces. Sci. China Math. 53, 2021–2030 (2010). https://doi.org/10.1007/s11425-010-3146-0

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  • DOI: https://doi.org/10.1007/s11425-010-3146-0

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