Abstract:We construct diffeological moduli stacks $\mathscr{M}_{Dol}(X)$ and $\mathscr{M}_{dR}(X)$ parametrizing smooth families of Higgs bundles and those of flat bundles, respectively, on a compact Kähler manifold $X$. We then establish an equivalence of stacks between diffeological substacks $\mathscr{M}^\mathscr{H}_{Dol} \subset \mathscr{M}_{Dol}(X)$ and $\mathscr{M}^\mathscr{H}_{dR}(X) \subset \mathscr{M}_{dR}(X)$, whose fibres over the point are the categories of semistable Higgs bundles, with the usual condition on Chern classes, and of flat bundles on $X$, respectively. $\mathscr{M}^\mathscr{H}_{Dol}(X)$ contains families of semistable Higgs bundles to points of which the classical correspondence of coarse moduli spaces does not extend continuously. This shows that the equivalence we provide is, in a sense, a common extension, in the context of diffeological moduli stacks, of both the homeomorphism of coarse moduli spaces, and of the equivalence of categories between semistable Higgs bundles and arbitrary flat bundles.
From: Mahmud Azam [view email]
[v1]
Mon, 15 Jun 2026 14:20:00 UTC (73 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。