An algebraic proof of the hyperplane property of the genus one GW-invariants of quintics

Abstract

Li-Zinger’s hyperplane property for reduced genus one GW-invariants of quintics states that the genus one GW-invariants of the quintic threefold is the sum of its reduced genus one GW-invariants and $1/12$ times its genus zero GW-invariants. We apply the theory of GW-invariants of stable maps with fields to give an algebro-geometric proof of this hyperplane property.