Abstract:Studying degenerations of moduli spaces of semistable principal bundles on smooth curves leads to the problem of studying moduli spaces on singular curves. In this note, we will see that the moduli spaces of $\delta$-semistable pseudo bundles on a nodal curve become, for large values of $\delta$, the moduli spaces of semistable singular principal bundles. The latter are reasonable candidates for degenerations and a potential basis for further developments as on irreducible nodal curves. In particular, we find a notion of semistability for principal bundles on reducible nodal curves. The understanding of the asymptotic behavior of $\delta$-semistability rests on a lemma from geometric invariant theory. The results allow for the construction of a universal moduli space of semistable singular principal bundles over the moduli space of stable curves. Due to recent work of Wilson, this universal moduli space has a close relation to the sheaf of algebras of conformal blocks.

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中文翻译：

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可约节点曲线上的奇异主丛

摘要：研究光滑曲线上半稳定主丛模空间的退化导致奇异曲线上模空间研究的问题。在本笔记中，我们将看到节点曲线上 $\delta$-半稳态伪丛的模空间，对于较大的 $\delta$ 值，变为半稳定奇异主丛的模空间。后者是退化的合理候选者，也是不可约节点曲线进一步发展的潜在基础。特别是，我们发现了可约节点曲线上主丛的半稳定性概念。对$\delta$-semistability 的渐近行为的理解依赖于几何不变理论的引理。结果允许在稳定曲线的模空间上构建半稳定奇异主丛的通用模空间。由于威尔逊最近的工作，这个通用模空间与共形块的代数束密切相关。

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