On the quantum cohomology of the plane, old and new

1995/08/23 by Ziv Ran, Ran, Ziv
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9508011

AMSTeX2.1

arxiv created 1995/10/23 · arxiv updated 2009/11/30

Abstract

We describe a method for counting maps of curves of given genus (and variable moduli) to \Bbb P², essentially by splitting the \Bbb P² in two; then specialising to the case of genus 0 we show that the method of quantum cohomology may be viewed as the 'mirror' of the former method where one splits the \Bbb P¹ rather than the \Bbb P², and we indicate a proof of the associativity of quantum multiplication based on this idea.

Related

• Quantum cohomology of complete intersections
• The quantum cohomology of blow-ups of P² and enumerative geometry
• The quantum cohomology of moduli space of \PGL₂-bundles on curves
• Quantum cohomology of the Hilbert scheme of points in the plane
• Quantum cohomology of moduli spaces of genus zero stable curves