QUANTUM COHOMOLOGY AND PERIODS

被引：39

作者：

Iritani, Hiroshi ^{[1
]}

机构：

[1] Kyoto Univ, Dept Math, Sakyo Ku, Kyoto 6068502, Japan

来源：

ANNALES DE L INSTITUT FOURIER | 2011年 / 61卷 / 07期

关键词：

quantum cohomology; mirror symmetry; Gamma class; K-theory; period; oscillatory integral; variation of Hodge structure; GKZ system; toric variety; orbifold; CALABI-YAU HYPERSURFACES; RIEMANN-ROCH; ORBIFOLD COHOMOLOGY; INTERSECTION THEORY; HODGE STRUCTURE; LEFSCHETZ; RING; CONJECTURE; MANIFOLDS;

D O I：

10.5802/aif.2798

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In a previous paper, the author introduced an integral structure in quantum cohomology defined by the K-theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle to the previous results, we find an explicit relationship between solutions to the quantum differential equation of toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism of variations of integral Hodge structure for a mirror pair of Calabi-Yau hypersurfaces (Batyrev's mirror).

引用

页码：2909 / 2958

页数：50

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