黎曼面局部Torelli定理的新证明

New Proofs of Local Torelli Theorems of Riemann Surfaces

利用亏格为g(g≥2)的闭曲面的Teichm(u|¨)ller空间上的Kuranishi坐标和闭黎曼面上全纯1-形式的显式形变公式,我们给出从Teichm(u|¨)ller空间到Siegel上半空间的周期映射的显示表达,从而得到了闭黎曼面的两个局部Torelli定理的新证明.

By use of the Kuranishi coordinates on the Teichmiiller space of closed surfaces of genus g with g≥2 and the explicit deformation formulae of holomorphic one-forms on close Riemann surfaces,we give explicit expressions of the period map from the Teichmiiller space to Siegel upper half space and obtain new proofs of two local Torelli theorems of closed Riemann surfaces.