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摘要翻译：
对于k>=2g的稳定的1点亏格g曲线的模空间上余切线类的k次方的简单边界表达式。该方法是在映射到射影线的模空间上进行虚拟定位。由此，构造了与稳定G+1曲线模空间的不可约边界因子相关的push-forward映射核中的非平凡重言类。g+1曲线的几何性质给出了g+1曲线Gromov-Witten理论中的通用方程。作为应用，我们证明了K.Liu和H.Xu最近提出的所有Gromov-Witten恒等式。
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英文标题：
《New topological recursion relations》
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作者：
Xiaobo Liu and Rahul Pandharipande
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最新提交年份：
2010
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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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英文摘要：
Simple boundary expressions for the k-th power of the cotangent line class on the moduli space of stable 1-pointed genus g curves are found for k >= 2g. The method is by virtual localization on the moduli space of maps to the projective line. As a consequence, nontrivial tautological classes in the kernel of the push-forward map associated to the irreducible boundary divisor of the moduli space of stable g+1 curves are constructed. The geometry of genus g+1 curves then provides universal equations in genus g Gromov-Witten theory. As an application, we prove all the Gromov-Witten identities conjectured recently by K. Liu and H. Xu.
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PDF链接：
https://arxiv.org/pdf/0805.4829
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