Genus-Zero Two-Point Hyperplane Integrals in the Gromov-Witten Theory

Details Genus-Zero Two-Point Hyperplane Integrals in the Gromov-Witten Theory Genus-Zero Two-Point Hyperplane Integrals in the Gromov-Witten Theory

2007-05-18

arxiv.org/abs/0705.2725v2

Mathematics

Algebraic Geometry

a number of changes to the introduction; 32 pages, 4 figures, 1 table

Scientific paper

In this paper we compute certain two-point integrals over a moduli space of stable maps into projective space. Computation of one-point analogues of these integrals constitutes a proof of mirror symmetry for genus-zero one-point Gromov-Witten invariants of projective hypersurfaces. The integrals computed in this paper constitute a significant portion in the proof of mirror symmetry for genus-one GW-invariants completed in a separate paper. These integrals also provide explicit mirror formulas for genus-zero two-point GW-invariants of projective hypersurfaces. The approach described in this paper leads to a reconstruction algorithm for all genus-zero GW-invariants of projective hypersurfaces.

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