The hyperplane property of genus 1 GW invariants of the quintic: an algebraic approach -- Jun Li, April 17, 2009

The hyperplane property of the GW-invariants of a quintic CY represents the virtual class of the moduli space of stable maps to the quintic as an Euler class of a bundle over the moduli space of stable maps to P^4. The genus 0 formulation was discovered by Kontsevich. This formulation fails for positive genus. In earlier work with Zinger, we proved that the hyperplane formula holds for reduced genus 1 GW-invariants. The approach was via analysis. In this talk, I will present an algebraic proof of this theorem. A conjecture on higher genus will be also discussed.