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

Nobuyoshi Takahashi

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

alg-geom 2008-02-03 v1 Algebraic Geometry

Authors: Nobuyoshi Takahashi

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 $\Bbb A^1$ , for $d\leq7$ (for $d=7$ under some assumption). We also count plane rational quartic curves intersecting $B$ at only one point.

Keywords

algebraic curves curves rational points on curves

Cite

@article{arxiv.alg-geom/9605007,
  title  = {Curves in the complement of a smooth plane cubic whose normalizations are $\Bbb A^1$},
  author = {Nobuyoshi Takahashi},
  journal= {arXiv preprint arXiv:alg-geom/9605007},
  year   = {2008}
}

Comments

AMS-TeX, 25 pages

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