The authors prove that, under a multiplicative genericity assumption, the OK condition on conjugacy classes suffices for solvability of the Deligne-Simpson problem, via a new relative spectral correspondence for parabolic Higgs bundles.
Topological Mirror Symmetry of Parabolic Hitchin Systems
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abstract
In this paper, we first prove the parabolic Beauvile-Narasimhan-Ramanan correspondence over an arbitrary field which generalizes the corresponding results over algebraically closed fields in [SWW22]. We use the correspondence and the p-adic integration methods developed by Groechenig- Wyss-Ziegler [GWZ20b] to prove the topological mirror symmetry for parabolic Hitchin systems on curves with arbitrary parabolic structures.
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Relative spectral correspondence for parabolic Higgs bundles and Deligne--Simpson problem
The authors prove that, under a multiplicative genericity assumption, the OK condition on conjugacy classes suffices for solvability of the Deligne-Simpson problem, via a new relative spectral correspondence for parabolic Higgs bundles.