On the quantum cohomology of the plane, old and new

Abstract

We describe a method for counting maps of curves of given genus (and variable moduli) to ${\mathbb{P}}^2$, essentially by splitting the ${\mathbb{P}}^2$ 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 ${\mathbb{P}}^1$ rather than the ${\mathbb{P}}^2$, and we indicate a proof of the associativity of quantum multiplication based on this idea.

AMSTeX2.1

Cited by in corpus (1)

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