Enumerative geometry of Calabi-Yau 4-folds

被引：67
|
作者：
Klemm, A. [1 ]
Pandharipande, R. [2 ]
机构：
[1] Univ Wisconsin, Dept Phys, Madison, WI 53706 USA
[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2008年 / 281卷 / 03期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1007/s00220-008-0490-9
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation. Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in P-5, are also studied. A complete solution of the Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic anomaly equation.
引用
收藏
页码：621 / 653
页数：33
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