博登-胡猜想恰好在八阶以下成立
The Boden-Hu conjecture holds precisely up to rank eight
摘要：
考虑光滑射影曲线上向量丛的模格式，该曲线在一点上具有抛物结构。Boden和Hu观察到，权重的轻微变化会导致模方案的去奇异化，他们强调，人们总是可以通过这种方式获得小的分辨率。本文本证明了这一猜想在某些情况下（包括所有束的秩高达8），并给出了反例在所有其他情况下（特别是在每一个秩超过8）。主要的工具是一个概括的外群涉及两个以上的quasiparabolic束。
英文摘要：
Consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point. Boden and Hu observed that a slight variation of the weights leads to a desingularisation of the moduli scheme, and they conjectured that one can always obtain a small resolution this way. The present text proves this conjecture in some cases (including all bundles of rank up to eight) and gives counterexamples in all other cases (in particular in every rank beyond eight). The main tool is a generalisation of Ext-groups involving more than two quasiparabolic bundles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
