an:06193031
Zbl 1300.14055
Iritani, Hiroshi
Quantum cohomology and periods
EN
Ann. Inst. Fourier 61, No. 7, 2909-2958 (2011).
0373-0956 1777-5310
2011
j
14N35 14D05 14D07 14J33 32G20 53D37
quantum cohomology; mirror symmetry; gamma class; \(K\)-theory; period; oscillatory integral; variation of Hodge structure; GKZ system; toric variety; orbifold
Motivated by Givental's work on mirror symmetry for toric complete intersections, the author finds an explicit relationship between solutions to the quantum differential equation and the periods for toric orbifold mirror pairs. The author also gives a detailed study of the mirror isomorphism of variations of Hodge structure for a mirror pair of Calabi-Yau hypersurfaces and shows that the A-model and B-model periods are equal. Several interesting questions are raised in the last section.
Hao Xu (Pittsburgh)