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