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- Title
Gromov-Witten theory and cycle-valued modular forms.
- Authors
Milanov, Todor; Yongbin Ruan; Yefeng Shen
- Abstract
In this paper, we review Teleman's work on lifting Givental's quantization of L(2)+ GL(H) action for semisimple formal Gromov-Witten potential into cohomological field theory level. We apply this to obtain a global cohomological field theory for simple elliptic singularities. The extension of those cohomological field theories over large complex structure limit are mirror to cohomological field theories from elliptic orbifold projective lines of weight (3, 3, 3), (2, 4, 4), (2, 3, 6). Via mirror symmetry, we prove generating functions of Gromov-Witten cycles for those orbifolds are cycle-valued (quasi)-modular forms.
- Subjects
QUANTIZATION methods (Quantum mechanics); GROMOV-Witten invariants; COHOMOLOGY theory; ELLIPTIC equations; ORBIFOLDS
- Publication
Journal für die Reine und Angewandte Mathematik, 2018, Vol 2017, Issue 735, p287
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2015-0019