Relative Gromov-Witten and maximal contact conics

Abstract

We discuss some properties of the relative Gromov--Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley's sextactic conics to any smooth plane curve $Y$. In particular, we compute the contribution, from double covers of inflectional lines, to a certain degree $2$ relative Gromov--Witten invariant relative to $Y$.