A remark by Daniel Ferrand on bundles on Fano threefolds

Gianfranco Casnati; Angelo Felice Lopez

A remark by Daniel Ferrand on bundles on Fano threefolds

Algebraic Geometry 2026-05-18 v3

Authors: Gianfranco Casnati , Angelo Felice Lopez

Abstract

Let $X$ be a Fano threefold with index $i_X$ and fundamental line bundle $\mathcal O_X(h)$ . We classify $\mu$ -semistable rank two bundles $\mathcal E$ on $X$ with $c_1(\mathcal E)=0$ , $h^0(\mathcal E) \ne 0$ and $h^1(\mathcal E(-\lceil\frac{i_X}{2}\rceil h))=0$ .

Keywords

fano threefold rank two bundle mu-semistable classification algebraic geometry

Cite

@article{arxiv.2212.04158,
  title  = {A remark by Daniel Ferrand on bundles on Fano threefolds},
  author = {Gianfranco Casnati and Angelo Felice Lopez},
  journal= {arXiv preprint arXiv:2212.04158},
  year   = {2026}
}

Comments

v.2: improved main theorem by describing the multiple structure in the case $i_X=2$, thanks to suggestion of anonymous referee. Added Remarks 3.6, 5.3 and more examples. v3: minor improvements

A remark by Daniel Ferrand on bundles on Fano threefolds

Abstract

Keywords

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