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arXiv · 2605.04160

Nonlinearizable embeddings of elliptic curves in rational surfaces

Simion Filip·Valentino Tosatti
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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.

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Simion Filip, Valentino Tosatti. 2026-05-05. Nonlinearizable embeddings of elliptic curves in rational surfaces. https://arxiv.org/abs/2605.04160

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