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arXiv · 1207.5697

New proofs of the Torelli theorems for Riemann surfaces

Kefeng Liu·Quanting Zhao·Sheng Rao
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Abstract

In this paper, by using the Kuranishi coordinates on the Teichm\"uller space and the explicit deformation formula of holomorphic one-forms on Riemann surface, we give an explicit expression of the period map and derive new differential geometric proofs of the Torelli theorems, both local and global, for Riemann surfaces.

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Kefeng Liu, Quanting Zhao, Sheng Rao. 2012-07-24. New proofs of the Torelli theorems for Riemann surfaces. https://arxiv.org/abs/1207.5697

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