曲线上半稳定与抛物线半稳定向量束的模栈的$\mathbb{A}^1$--连通性
代数几何
2026-04-22 v3
摘要
设C为特征为g≥2的不可约光滑射影曲线。我们证明了固定秩和行列式的C上半稳定向量束的模栈是--连通的。我们还证明了具有固定行列式和给定沿C上点集合的抛物线数据的准抛物线向量束的模栈也是--连通的。此外，对于小且一般的权重且，--半稳定抛物线向量束的开子模栈也是--连通的。
引用
@article{arxiv.2512.14464,
title = {$\mathbb{A}^1$--connectedness of moduli stack of semi-stable and parabolic semi-stable vector bundles over a curve},
author = {Sujoy Chakraborty and Saurav Holme Choudhury},
journal= {arXiv preprint arXiv:2512.14464},
year = {2026}
}
备注
Substantial changes have been made in Section 2 to address a gap in the earlier version. The main result in Section 2 remains unchanged. In Section 3, some additional assumptions on weights have been added for the final theorem. Comments are welcome