The Picard group of the moduli space of curves with level structures
The Picard group of the moduli space of curves with level structures
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具有水平结构的曲线模空间的皮卡德群
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Andrew Putman
中科院分区：
文献类型：
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作者：
Andrew Putman
对于4 L和g大，我们计算了具有水平L结构的曲线模空间和主极化交换簇的积分Picard群.特别是，我们确定了这些模空间上的标准线丛的整除性质，并计算了映射类群的水平L子群的第二整上同调群（在以前的论文中，作者合理地确定了这一点）。这需要计算的阿贝尔化的水平L子群的映射类组，推广以前的结果Perron，佐藤，和作者。最后，沿着这种方法，我们计算了模L辛群的第一同调群，其系数在伴随表示中。
For 4 L and g large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level L structures. In particular, we determine the divisibility properties of the standard line bundles over these moduli spaces and we calculate the second integral cohomology group of the level L subgroup of the mapping class group (in a previous paper, the author determined this rationally). This entails calculating the abelianization of the level L subgroup of the mapping class group, generalizing previous results of Perron, Sato, and the author. Finally, along the way we calculate the first homology group of the mod L symplectic group with coefficients in the adjoint representation.