Communications in Analysis and Geometry

Volume 17 (2009)

Number 5

Genus-zero two-point hyperplane integrals in the Gromov–Witten theory

Pages: 955 – 999



Aleksey Zinger (Department of Mathematics, State University of New York, Stony Brook)


In this paper, we compute certain two-point integrals overa moduli space of stable maps into projective space.Computation of one-point analogs of these integralsconstitutes a proof of mirror symmetry for genus-zeroone-point Gromov--Witten (GW) invariants of projectivehypersurfaces. The integrals computed in this paperconstitute a significant portion in the proof of mirrorsymmetry for genus-{\it{one}} GW-invariants completed in aseparate paper. These integrals also provide explicitmirror formulas for genus-zero {\it two}-pointGW-invariants of projective hypersurfaces. The approachdescribed in this paper leads to a reconstruction algorithmfor all genus-zero GW-invariants of projectivehypersurfaces.

Published 1 January 2009