Curves in the complement of a smooth plane cubic whose normalizations are ${\mathbb{A}}^1$

Abstract

For a smooth plane cubic $B$, we count curves $C$ of degree $d$ such that the normalizations of $C\backslash B$ are isomorphic to ${\mathbb{A}}^1$, for $d\le 7$ (for $d=7$ under some assumption). We also count plane rational quartic curves intersecting $B$ at only one point.

AMS-TeX, 25 pages

References in corpus (1)

• On the intersections of rational curves with cubic plane curves

Cited by in corpus (4)

• On the multiplicity of reducible relative stable morphisms
• Log BPS numbers of log Calabi-Yau surfaces
• On the intersections of rational curves with cubic plane curves
• Mirror symmetry and C^\times