Stable maps to Looijenga pairs built from the plane

Abstract

Choosing a normal crossings anticanonical divisor of ${\mathbb{P}}^2$ leads to four log Calabi-Yau surfaces, three of which are Looijenga pairs. In this survey article, I describe how to count rational curves in these that intersect each component of the divisor in one point of maximal tangency.

14 pages, 8 figures