The Reduced Genus 1 Gromov-witten Invariants of Calabi-yau Hypersurfaces
نویسنده
چکیده
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 M̃1,1(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
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