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arxiv: 0904.3430 · v1 · submitted 2009-04-22 · 🧮 math.AG

Connections for weighted projective lines

classification 🧮 math.AG
keywords categorycoherentconnectionlenzingprojectiveweightedalgebrabundle
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We introduce a notion of a connection on a coherent sheaf on a weighted projective line (in the sense of Geigle and Lenzing). Using a theorem of Huebner and Lenzing we show, under a mild hypothesis, that if one considers coherent sheaves equipped with such a connection, and one passes to the perpendicular category to a nonzero vector bundle without self-extensions, then the resulting category is equivalent to the category of representations of a deformed preprojective algebra.

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