Parameter spaces for curves on surfaces and enumeration of rational curves

被引：14

作者：

Caporaso, L ^{[1
]}

Harris, J

机构：

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] Univ Rome 2, Dipartimento Matemat, I-00133 Rome, Italy

来源：

COMPOSITIO MATHEMATICA | 1998年 / 113卷 / 02期

关键词：

rational surface; rational curve; enumerative geometry; Severi variety; cross-ratio method;

D O I：

10.1023/A:1000401119940

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let S be a smooth, minimal rational surface. The geometry of the Severi variety parametrising irreducible, rational curves in a given linear system on S is studied. The results obtained are applied to enumerative geometry, in combination with ideas from Quantum Cohomology. Formulas enumerating rational curves are found, some of which generalise Kontsevich's formula for plane curves.

引用

页码：155 / 208

页数：54