Enumeration of Elliptic Curves via Elliptic Gromov-Witten Invariants of Four Dimensional Projective Fano Hypersurfaces

Abstract

In this paper, we propose a conjecture that clarifies the relationship between the number of degree d elliptic curves in complex four-dimensional projective Fano hypersurfaces and their degree d elliptic Gromov-Witten (GW) invariants. The elliptic GW invariants are computed using the elliptic virtual structure constants proposed in our previous works.

30 pages, Latex, Doi of the package of Kuwata's Mathematica files has been changed, minor errors are corrected