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The Segre invariant and Brill-Noether theory on Hirzebruch surfaces
Abstract
We study the Segre invariant on rank two H-stable vector bundles with fixed Chern classes on Hirzebruch surfaces Σn. For each vector bundle on these surfaces, we determine the possible values of the Segre invariant and compute the number of global sections of these bundles and present applications to Brill-Noether Theory.
Related
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- A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces
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BibTeX
@misc{riveravega2026segre,
title = {{The Segre invariant and Brill-Noether theory on Hirzebruch surfaces}},
author = {Mauricio Rivera-Vega},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27769},
eprint = {2608.27769},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27769},
}
RIS
TY - UNPB
TI - The Segre invariant and Brill-Noether theory on Hirzebruch surfaces
AU - Mauricio Rivera-Vega
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27769
UR - https://arxiv.org/abs/2608.27769
AB - We study the Segre invariant on rank two H-stable vector bundles with fixed Chern classes on Hirzebruch surfaces Σ_n. For each vector bundle on these surfaces, we determine the possible values of the Segre invariant and compute the number of global sections of these bundles and present applications to Brill-Noether Theory.
ER -