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Balancedness of Normal Bundles of Rational Curves in Grassmannians
Abstract
In projective space ℙr, the normal bundle of a general rational curve of any degree d ≥ r is balanced except over fields of characteristic 2. In arXiv:2404.08102, Coskun, Larson, and Vogt found counterexamples to the naive generalization of this statement to general rational curves in Grassmannians and proposed a conjecture for when the normal bundle is balanced. In this paper, we prove their conjecture for the Grassmannians $G(2, 4)$, $G(2, 5)$, and $G(2, 6)$.
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BibTeX
@misc{cao2026balancedness,
title = {{Balancedness of Normal Bundles of Rational Curves in Grassmannians}},
author = {An Cao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19381},
eprint = {2609.19381},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19381},
}
RIS
TY - UNPB
TI - Balancedness of Normal Bundles of Rational Curves in Grassmannians
AU - An Cao
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19381
UR - https://arxiv.org/abs/2609.19381
AB - In projective space ℙ^r, the normal bundle of a general rational curve of any degree d ≥ r is balanced except over fields of characteristic 2. In arXiv:2404.08102, Coskun, Larson, and Vogt found counterexamples to the naive generalization of this statement to general rational curves in Grassmannians and proposed a conjecture for when the normal bundle is balanced. In this paper, we prove their conjecture for the Grassmannians $G(2, 4)$, $G(2, 5)$, and $G(2, 6)$.
ER -