Reduced Genus-One Gromov-Witten Invariants and Applications
I will describe a "part" of the standard GW-invariant, which under
ideal conditions counts genus-one curves without any genus-zero contribution.
In contrast to the standard GW-invariant, the resulting reduced GW-invariant has the expected behavior with respect to certain embeddings. These invariants have applications to computing the standard genus-one GW-invariants of complete intersections as well as some enumerative genus-one invariants of sufficiently positive complete intersections. The former application opens a way to try to verify the mirror symmetry prediction for genus-one curves in Calabi-Yau therefolds.