2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138371We 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.13 pages; minor changes onlyAlgebraic Geometry14H60, 16G20text