正规函数与Gross-Schoen圈的高度
Normal functions and the height of Gross-Schoen cycles
摘要：
我们证明了一个公式的一个变种由于S。张先生将尖曲线上Gross-Schoen圈的Beilinson-Bloch高度与其相对对偶层的自相交联系起来。在我们的方法中，Gross-Schoen循环的高度作为合适的Bloch线丛的度出现。证明了该线丛的陈式是非负的，并计算了它在紧致型点稳定曲线的模空间的Picard群中的类.基本的工具是正规函数和与泛雅可比上同调相关的双扩张。
英文摘要：
We prove a variant of a formula due to S. Zhang relating the Beilinson-Bloch height of the Gross-Schoen cycle on a pointed curve with the self-intersection of its relative dualizing sheaf. In our approach the height of the Gross-Schoen cycle occurs as the degree of a suitable Bloch line bundle. We show that the Chern form of this line bundle is non-negative, and we calculate its class in the Picard group of the moduli space of pointed stable curves of compact type. The basic tools are normal functions and biextensions associated to the cohomology of the universal jacobian.
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