Mathematics > Algebraic Geometry
[Submitted on 11 Jul 2018 (v1), last revised 3 Jul 2023 (this version, v3)]
Title:Arithmetic and metric aspects of open de Rham spaces
View PDFAbstract:In this paper we determine the motivic class--in particular, the weight polynomial and conjecturally the Poincaré polynomial--of the open de Rham space, defined and studied by Boalch, of certain moduli spaces of irregular meromorphic connections on the trivial rank $n$ bundle on $\mathbb{P}^1$. The computation is by motivic Fourier transform. We show that the result satisfies the purity conjecture, that is, it agrees with the pure part of the conjectured mixed Hodge polynomial of the corresponding wild character variety. We also identify the open de Rham spaces with quiver varieties with multiplicities of Yamakawa and Geiss--Leclerc--Schröer. We finish with constructing natural complete hyperkähler metrics on them, which in the $4$-dimensional cases are expected to be of type ALF.
Submission history
From: Dimitri Wyss [view email][v1] Wed, 11 Jul 2018 10:25:52 UTC (66 KB)
[v2] Mon, 6 Feb 2023 23:21:34 UTC (71 KB)
[v3] Mon, 3 Jul 2023 23:27:52 UTC (71 KB)
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