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Kac's Theorem for weighted projective lines

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arxiv math/0512078 v2 pith:7SHE25KY submitted 2005-12-04 math.AG

Kac's Theorem for weighted projective lines

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keywords algebraprojectivetheoremweightedcoherentlinessheavesanalogue
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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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  1. Topological model for derived category associated to sphere with four binaries

    math.RT 2026-07 conditional novelty 6.0

    Indecomposable rigid objects in the derived category of the (2,2,2,2)-weighted projective line are shown to correspond to graded simple arcs on a sphere with four binaries, with Hom-dimensions given by oriented inters...