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.
Katz’s middle convolution algorithm
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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.