Geodesic
Kac's Theorem for weighted projective lines
Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1331-1345 Cet article a éte moissonné depuis la source EMS Press

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We prove an analogue of Kac’s Theorem, describing the dimension types of indecomposable coherent sheaves (or parabolic bundles) over weighted projective lines in terms of root systems for loop algebras of Kac–Moody Lie algebras. 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. We use these elements in the proof of our analogue of Kac’s Theorem.
DOI : 10.4171/jems/232
Classification : 14-XX, 16-XX, 00-XX
Keywords: Weighted projective line, parabolic bundle, Kac–Moody Lie algebra, loop algebra, Hall algebra 
@article{JEMS_2010_12_6_a0,
     author = {William Crawley-Boevey},
     title = {Kac's {Theorem} for weighted projective lines},
     journal = {Journal of the European Mathematical Society},
     pages = {1331--1345},
     year = {2010},
     volume = {12},
     number = {6},
     doi = {10.4171/jems/232},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/232/}
}
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William Crawley-Boevey. Kac's Theorem for weighted projective lines. Journal of the European Mathematical Society, Tome 12 (2010) no. 6, pp. 1331-1345. doi: 10.4171/jems/232

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