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Kac's Theorem for weighted projective lines

William Crawley-Boevey
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Abstract

We prove an analogue of Kac's Theorem, describing the dimension vectors of indecomposable coherent sheaves, or parabolic bundles, over weighted projective lines. We use a theorem of Peng and Xiao to associate a Lie algebra to the category of coherent sheaves for a weighted projective line over a finite field, and find elements of this Lie algebra which satisfy the relations defining the loop algebra of a Kac-Moody Lie algebra.

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William Crawley-Boevey. 2007-09-20. Kac's Theorem for weighted projective lines. https://arxiv.org/abs/math/0512078

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