PreprintarXiv licencearXiv
Canonical extensions of ruled surfaces over elliptic curves
Abstract
Let L be a line bundle of negative degree on an elliptic curve E. While the ruled surface M := ℙ(𝒪E ⊕ L) is one of the simplest varieties in algebraic geometry, its tangent bundle TM 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 ZM which allows us to show that ZM is not Stein.
Related
- On ruled normal surfaces associated with rectifying curves
- Computing S(X) for Ruled Surfaces Defined by Stable Bundles on Curves of Genus 2
- Computing the Iwasawa μ-Invariants for Elliptic Curves over ℤ2-Extensions
- Torsion groups of rational elliptic curves over ℤp-extensions of quadratic fields: the p≤ 5 case
- Torsion growth of rational elliptic curves over Zp-extensions of quadratic fields
BibTeX
@misc{denisi2026canonical,
title = {{Canonical extensions of ruled surfaces over elliptic curves}},
author = {Francesco Antonio Denisi and Andreas Höring},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03048},
eprint = {2610.03048},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03048},
}
RIS
TY - UNPB
TI - Canonical extensions of ruled surfaces over elliptic curves
AU - Francesco Antonio Denisi
AU - Andreas Höring
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03048
UR - https://arxiv.org/abs/2610.03048
AB - Let L be a line bundle of negative degree on an elliptic curve E. While the ruled surface M := ℙ(𝒪_E ⊕ 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.
ER -