Resumen de On the quantum cohomology of the plane, old and new and a K3 analogue

Ziv Ran

• 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 half; 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 $\mathbb{P}^2$; finally we indicate an analogue of the former method where $\mathbb{P}^2$ is replaced by a K3 quartic.