Nonlinearizable embeddings of elliptic curves in rational surfaces

Simion Filip; Valentino Tosatti

Nonlinearizable embeddings of elliptic curves in rational surfaces

Dynamical Systems 2026-05-07 v1 Algebraic Geometry Complex Variables

Authors: Simion Filip , Valentino Tosatti

Abstract

We show that for any smooth cubic in $\mathbb{P}^2$ , there exists a dense $G_\delta$ set of configurations of 9 distinct points such that blowing up $\mathbb{P}^2$ at these 9 points, the strict transform of the cubic is not linearizable and has nontorsion normal bundle. This answers a problem raised by Ogus in 1975.

Keywords

elliptic curves rational surfaces nonlinearizable embeddings cubic curves normal bundle

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@article{arxiv.2605.04160,
  title  = {Nonlinearizable embeddings of elliptic curves in rational surfaces},
  author = {Simion Filip and Valentino Tosatti},
  journal= {arXiv preprint arXiv:2605.04160},
  year   = {2026}
}

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30 pages

Nonlinearizable embeddings of elliptic curves in rational surfaces

Abstract

Keywords

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