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

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.