Enumeration of rational plane curves tangent to a smooth cubic

Abstract

We compute the number of rational degree d plane curves having prescribed fixed and moving contacts to a smooth plane cubic E. We use twisted stable maps to the stack P E , r 2 for r large, where P E , r 2 is the rth root of P 2 along E. We prove that certain Gromov–Witten invariants of this stack are enumerative, and establish recursive formulas for these numbers.