The reduced genus 1 Gromov-Witten invariants of Calabi-Yau hypersurfaces

By A. Zinger. 2007

134 citations recorded by the source corpus.

0. Introduction 691 0.1. Mirror symmetry predictions for a quintic threefold 691 0.2. Computing GW-invariants of hypersurfaces 693 0.3. Mirror symmetry formulas for projective CY-hypersurfaces 695 1. Equivariant cohomology and stable maps 698 1.1. Definitions and notation 698 1.2. Setup for localization computation on M1,1(P, d) 701 1.3. Contributions from fixed loci, I 704 1.4. Contributions from fixed loci, II 708 2. Localization computations 712 2.1. Regularizable power series in rational functions 712 2.2. Regularizability of GW generating functions 714 2.3. Proofs of Propositions 1.1 and 1.2 717 3. Algebraic computations 721 3.1. Linear independence in symmetric rational functions 722 3.2. The genus 0 generating functions 723 3.3. Proof of Theorem 3 725 Appendix A. Some combinatorics 730 Appendix B. Comparison of mirror symmetry formulations 733 Acknowledgments 736 References 736

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c81b8985315a79fe84c2d9d27ffd20ee0c582cd8

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In Geometry and Topology

1. R. Pandharipande
2. Y. Ruan
3. Davesh Maulik
4. A. Chiodo
5. A. Zinger
6. Bumsig Kim
7. A. Okounkov
8. Aaron Pixton

In Mathematical Physics

1. R. Pandharipande
2. Davesh Maulik
3. Y. Ruan
4. A. Zinger
5. A. Chiodo
6. Bumsig Kim
7. A. Okounkov
8. Aaron Pixton

Citations in the corpus

• Reduced genus-one Gromov-Witten invariants (2005, methodology): “Combining [LZ, Theorem 1.1] for the reduced genus-one invariants constructed in this paper with the desingularization of Vakil and the author in [VaZ1] and Theorem 1.1 below, the author nally conrms the 1993 mirror symmetry of Bershadsky-Cecotti-Ooguri-Vafa [BCOV] for the genus-one GW-invariants of ”
• Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations (2008, methodology): “single invariant and when one needs to effectively compute the full higher genus Gromov–Witten theory. The genus-one theory has been computed only recently by A. Zinger after a great deal of hard work [Zi09]. Computations in higher genera are out of mathematicians’ reach for the moment. There is a ph”
• Gromov-Witten theory and Noether-Lefschetz theory (2007, background): “er on automorphic functions [6] which underlies [7] was motivated in part by the work of Harvey 2While the paper [7, 29] have considerable overlap, we will follow the point of view of Borcherds. 3See [54] for a different mathematical approach to genus 1 invariants for complete intersections. GROMOV-W”
• Logarithmic Stable Maps (2008, background): “The hyperplane section principle for reduced genus 1 Gromov-Witten invariants and the comparisons between reduced and standard genus 1 invariants are accomplished in [23, 35, 36 , 37].”