Normal Functions and the Geometry of Moduli Spaces of Curves
Normal Functions and the Geometry of Moduli Spaces of Curves
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正规函数和曲线模空间的几何
DOI：
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发表时间：
2011
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通讯作者：
R. Hain
中科院分区：
文献类型：
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作者：
R. Hain
本文利用Griffiths意义下的正规函数来解决和细化曲线的模空间的几何问题。第一个应用是关于Eliashberg提出的一个问题：计算泛雅可比零截面沿Jac(C)中取[C；x_1，…，x_n]到和d_j x_j的截面M_{g，n}^c的上同调中的类，其中d_1+…+d_n=0。第二个应用是Moriwaki所发现的斜率不等式。还讨论了高度跳跃及其与坡度不均的相关性。
In this paper normal functions (in the sense of Griffiths) are used to solve and refine geometric questions about moduli spaces of curves. The first application is to a problem posed by Eliashberg: compute the class in the cohomology of M_{g,n}^c of the pullback of the zero section of the universal jacobian along the section that takes [C;x_1,...,x_n] to Sum d_j x_j in Jac (C), where d_1 + ... + d_n = 0. The second application is to slope inequalities of the type discovered by Moriwaki. There is also a discussion of height jumping and its relevance to slope inequalilties.