Bergman度量在奇异纤维上的变分

Variation of Bergman Metrics Along Singular Fibers

在本文中,我们将考虑推广至具有典范奇点的复解析簇上的缠多典则丛奇异度量的比较问题.对在复平面单位圆盘上的代数纤维,我们将证明若在具有典范奇点的复解析簇纤维上缠线丛的奇异度量斜率为零,则定义于代数纤维上的相对缠m-Bergman度量在该解析簇纤维上的限制与其内蕴缠m-Bergman度量相等.

In this paper,we study a generalized comparison question about singular metrics of twisted pluricanonical bundles over complex varieties with canonical singularities.We prove that for an algebraic fibration over the unit disc,the restriction of the twisted relative m-Bergman metric on a singular fiber with canonical singularities at worst coincides with the intrinsic twisted m-Bergman metric on itself,provided that the singular metric on the twisted line bundle has slope zero at each point belonging to the singular fiber.