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arXiv · 2610.03048

Canonical extensions of ruled surfaces over elliptic curves

Francesco Antonio Denisi·Andreas Höring
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Abstract

Let $L$ be a line bundle of negative degree on an elliptic curve $E$. While the ruled surface $M := \mathbb P(\mathcal O_E \oplus L)$ is one of the simplest varieties in algebraic geometry, its tangent bundle $T_M$ is surprisingly complex: we first show that the ring of symmetric tensors is not finitely generated. We then construct a holomorphic function on the canonical extension $Z_M$ which allows us to show that $Z_M$ is not Stein.

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Francesco Antonio Denisi, Andreas Höring. 2026-10-02. Canonical extensions of ruled surfaces over elliptic curves. https://arxiv.org/abs/2610.03048

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