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arXiv · 2604.06991

The Deligne-Simpson problem via 2-Calabi-Yau categories

Lucien Hennecart
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Abstract

We provide a short proof of the necessity of Crawley-Boevey's condition in his solution to the Deligne-Simpson problem. The proof relies on the local neighbourhood theorem for $2$-Calabi-Yau categories due to Davison together with Crawley-Boevey's sufficient condition for the existence of local systems with prescribed conjugacy classes of monodromy around the punctures.

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Lucien Hennecart. 2026-04-08. The Deligne-Simpson problem via 2-Calabi-Yau categories. https://arxiv.org/abs/2604.06991

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