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PreprintCC0arXiv

A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces

  • L. Roa-Leguizamón
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Abstract

The aim of this paper is to study the Segre invariant for rank $2$ vector bundles on Hirzebruch surfaces 𝔽e, e ≥ 0. We give necessary conditions in order to determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle on 𝔽e with fixed Chern classes. We compute a bound of the dimensions of the strata whenever are non-empty. Finally, we present applications to Brill-Noether Theory and describe differences between moduli spaces under change of polarization for rank $2$ vector bundles on 𝔽e.

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Cite

BibTeXRIS
BibTeX
@misc{roaleguizamon2026note,
  title = {{A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces}},
  author = {L. Roa-Leguizamón},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30236},
  eprint = {2608.30236},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30236},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces
AU  - L. Roa-Leguizamón
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30236
UR  - https://arxiv.org/abs/2608.30236
AB  - The aim of this paper is to study the Segre invariant for rank $2$ vector bundles on Hirzebruch surfaces 𝔽_e, e ≥ 0. We give necessary conditions in order to determine what numbers can appear as the Segre Invariant of a rank $2$ vector bundle on 𝔽_e with fixed Chern classes. We compute a bound of the dimensions of the strata whenever are non-empty. Finally, we present applications to Brill-Noether Theory and describe differences between moduli spaces under change of polarization for rank $2$ vector bundles on 𝔽_e.
ER  -