New proofs of the Torelli theorems for Riemann surfaces

Abstract

In this paper, by using the Kuranishi coordinates on the Teichmüller 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.

arXiv commentA revised version, 21 pages; All comments are welcome

References in corpus (2)

• Strict and non strict positivity of direct image bundles
• Quasi-isometry and deformations of Calabi-Yau manifolds

Cited by in corpus (1)

• Extension formulas and deformation invariance of Hodge numbers