Compactifications of Hurwitz Spaces
Compactifications of Hurwitz Spaces
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Hurwitz 空间的紧化
DOI：
10.1093/imrn/rnt060
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发表时间：
2012
影响因子：
1
通讯作者：
Anand Deopurkar
中科院分区：
文献类型：
--
作者：
Anand Deopurkar
本文构造了亏格为g的曲线的Hurwitz空间H^d_{g/h}$的几种模紧化，表示为亏格为h的曲线的d$-单支复盖.这些紧化是通过允许覆盖的分支点碰撞到一个可变的程度。如果$d = 2，3$，或者如果允许相对较少的冲突，则它们表现得非常好。作为特殊情况，我们恢复扭曲的容许覆盖的阿布拉莫维奇，科尔蒂和Vistoli和空间的超椭圆曲线的Fedorchuk的空间。
We construct several modular compactifications of the Hurwitz space $H^d_{g/h}$ of genus $g$ curves expressed as $d$-sheeted, simply branched covers of genus $h$ curves. These compactifications are obtained by allowing the branch points of the covers to collide to a variable extent. They are very well-behaved if $d = 2, 3$, or if relatively few collisions are allowed. We recover as special cases the spaces of twisted admissible covers of Abramovich, Corti and Vistoli and the spaces of hyperelliptic curves of Fedorchuk.