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arXiv · 2310.15652

Semiprojectivity of the moduli of principal $G$-bundles with $λ$-connections

Sumit Roy·Anoop Singh
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Abstract

Let $X$ be a compact connected Riemann surface of genus $g \geq 2$ and $G$ a connected reductive affine algebraic group over $\mathbb{C}$. We prove the semiprojectivity of the moduli spaces of semistable $G$-Higgs bundles and $G$-bundles with $λ$-connections of fixed topological type $d\in π_1(G)$. As an application, in the smooth case we describe the resulting Bialynicki - Birula decomposition and derive cohomological and motivic consequences.

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Sumit Roy, Anoop Singh. 2026-03-01. Semiprojectivity of the moduli of principal $G$-bundles with $λ$-connections. https://arxiv.org/abs/2310.15652

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