曲线的Bergman核和周期图
Bergman kernel and period map for curves
摘要：
对于任何对称空间，Siegel上半空间的切空间都被赋予了一个来自李代数上的李括号的运算。我们考虑通过Torelli映射将这种操作拉回到曲线的模空间。我们的特征在于它的曲线的几何形状，使用的Bergman内核形式相关联的曲线。已知超椭圆轨迹外的Torelli映射的第二基本型可以看作是与某个亚纯型的乘积。我们的第二个结果说，伯格曼核形式是调和代表-在适当的意义上-这个亚纯形式。
英文摘要：
As for any symmetric space the tangent space to Siegel upper-half space is endowed with an operation coming from the Lie bracket on the Lie algebra. We consider the pull-back of this operation to the moduli space of curves via the Torelli map. We characterize it in terms of the geometry of the curve, using the Bergman kernel form associated to the curve. It is known that the second fundamental form of the Torelli map outside the hyperelliptic locus can be seen as the multiplication by a certain meromorphic form. Our second result says that the Bergman kernel form is the harmonic representative - in a suitable sense - of this meromorphic form.
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