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摘要翻译：
本文证明了具有6个标记点的稳定有理曲线的模空间$\bar{M}{0,6}$的Cox环是由与稳定的亏格3曲线的模空间$\bar{M}_3$中超椭圆轨迹的拉回的边界因子和因子相对应的截面有限生成的，通过识别3对点将一条6点有理曲线发送到一条具有3个结点的曲线的态射。特别地，给出了Hassett和Tschinkel关于$\bar{M}{0,6}$的有效锥由上述因子生成的结果的自包含证明。
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英文标题：
《The Cox Ring of $\bar{M}_{0,6}$》
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作者：
Ana-Maria Castravet
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
We prove that the Cox ring of $\bar{M}_{0,6}$, the moduli space of stable, rational curves with 6 marked points, is finitely generated by sections corresponding to the boundary divisors and divisors which are pull-backs of the hyperelliptic locus in $\bar{M}_3$, the moduli space of stable, genus 3 curves, via morphisms that send a 6-pointed rational curve to a curve with 3 nodes by identifying 3 pairs of points. In particular, this gives a self-contained proof of Hassett and Tschinkel's result about the effective cone of $\bar{M}_{0,6}$ being generated by the above mentioned divisors.
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PDF链接：
https://arxiv.org/pdf/0705.0070
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