The zero section of the universal semiabelian variety and the double ramification cycle
The zero section of the universal semiabelian variety and the double ramification cycle
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通用半阿贝尔簇的零截面和双分枝循环
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
D. Zakharov
中科院分区：
文献类型：
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作者：
S. Grushevsky;D. Zakharov
研究了主极化阿贝尔变种普适族的部分紧化边界的Chow环。我们刻画了由除数类生成的子环，并计算了泛零截面的部分紧化类，证明它位于这个子环中。我们的公式推广了泛非紧化族的零截面的结果。
PPAV普适族的部分紧化可以看作是PPAV模空间的任意环向紧化的前两个边界层。我们的公式提供了一个程序的第一步，通过对亏格的归纳来理解PPAV的模环向紧化的Chow群，特别是完美圆锥紧化的Chow群。通过限制曲线的雅可比轨迹，我们的结果推广了Hain关于双分支(两分支点)循环的结果。
We study the Chow ring of the boundary of the partial compactification of the universal family of principally polarized abelian varieties (ppav). We describe the subring generated by divisor classes, and compute the class of the partial compactification of the universal zero section, which turns out to lie in this subring. Our formula extends the results for the zero section of the universal uncompactified family.
The partial compactification of the universal family of ppav can be thought of as the first two boundary strata in any toroidal compactification of the moduli space of ppav. Our formula provides a first step in a program to understand the Chow groups of toroidal compactifications of the moduli of ppav, especially of the perfect cone compactification, by induction on genus. By restricting to the locus of Jacobians of curves, our results extend the results of Hain on the double ramification (two-branch-point) cycle.
影响因子：
3.1
作者：
S. Grushevsky;K. Hulek
通讯作者：
S. Grushevsky;K. Hulek
影响因子：
3.1
作者：
D. Petersen;O. Tommasi
通讯作者：
D. Petersen;O. Tommasi