Absolute and relative Gromov-Witten invariants of very ample hypersurfaces
Absolute and relative Gromov-Witten invariants of very ample hypersurfaces
复制标题
非常充足的超曲面的绝对和相对 Gromov-Witten 不变量
DOI：
10.1215/s0012-7094-02-11521-x
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发表时间：
1999
影响因子：
2.5
通讯作者：
A. Gathmann
中科院分区：
文献类型：
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作者：
A. Gathmann
对于任意光滑复射影簇X和X中的光滑非常充裕超曲面Y，我们用代数几何的方法给出了Y在X中亏格为零的相对Gromov-Witten不变量的技巧.我们证明了相对稳定映射的模空间的Chow群中的圈的相等性，它将这些相对不变量与X和Y的Gromov-Witten不变量联系起来。给定X的Gromov-Witten不变量，我们证明了这些关系足以计算所有的相对不变量，以及Y的所有亏格为零的Gromov-Witten不变量，其同调和上同调类由X诱导。
For any smooth complex projective variety X and smooth very ample hypersurface Y in X, we develop the technique of genus zero relative Gromov-Witten invariants of Y in X in algebro-geometric terms. We prove an equality of cycles in the Chow groups of the moduli spaces of relative stable maps that relates these relative invariants to the Gromov-Witten invariants of X and Y. Given the Gromov-Witten invariants of X, we show that these relations are sufficient to compute all relative invariants, as well as all genus zero Gromov-Witten invariants of Y whose homology and cohomology classes are induced by X.