Kac's Theorem for weighted projective lines
Algebraic Geometry
2007-09-20 v2
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.
Cite
@article{arxiv.math/0512078,
title = {Kac's Theorem for weighted projective lines},
author = {William Crawley-Boevey},
journal= {arXiv preprint arXiv:math/0512078},
year = {2007}
}
Comments
13 pages; minor changes only