Bott’s formula and enumerative geometry
Bott’s formula and enumerative geometry
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Bott 公式和枚举几何
DOI：
10.1090/s0894-0347-96-00189-0
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发表时间：
1994
影响因子：
3.9
通讯作者：
S. A. Strømme
中科院分区：
文献类型：
--
作者：
G. Ellingsrud;S. A. Strømme
我们概述了一种使用 Bott 留数公式计算具有环面动作的平滑簇上的交集数的策略。作为一个例子，计算了射影空间中某些一般完全交集上的扭曲三次曲线和椭圆四次曲线的 Gromov-Witten 数。结果与镜像对称计算的预测一致。我们还计算度数小于 10 的平面曲线线性系统中某些轨迹的度数，例如对应于线性形式的幂和的那些轨迹，以及带有内切多边形的曲线。 MATHEMATICAL INSTITUTE, UNIVERSITY OF OSLO, P. 0. Box 1053, N-0316 OSLO, NORWAY 电子邮件地址：ellingsr0math.uio .no MATHEMATICAL INSTITUTE, UNIVERSITY OF BERGEN, ALLEG 55, N-5007 BERGEN, NORWAY 电子邮件地址：strommati i.uib.no此内容于 2016 年 4 月 12 日星期二 10:23:14 UTC 从 157.55.39.29 下载 所有使用均遵循 http://about.jstor.org/terms
We outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of Bott. As an example, Gromov-Witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are computed. The results are consistent with predictions made from mirror symmetry compu- tations. We also compute degrees of some loci in the linear system of plane curves of degrees less than 10, like those corresponding to sums of powers of linear forms, and curves carrying inscribed polygons. MATHEMATICAL INSTITUTE, UNIVERSITY OF OSLO, P. 0. Box 1053, N-0316 OSLO, NORWAY E-mail address: ellingsr0math.uio .no MATHEMATICAL INSTITUTE, UNIVERSITY OF BERGEN, ALLEG 55, N-5007 BERGEN, NORWAY E-mail address: strommeti i.uib.no This content downloaded from 157.55.39.29 on Tue, 12 Apr 2016 10:23:14 UTC All use subject to http://about.jstor.org/terms