Norbert Hoffmann
Verallgemeinerte Garben \"uber einer algebraischen Kurve
Preprint series: Mathematica Gottingensis
MSC:
14F05 Vector bundles, sheaves, related construction, See Also {18F20, 32Lxx, 46M20}
14H60 Vector bundles on curves, See also {14F05}
Abstract: The subject of this paper is the construction of an abelian category, the category of
generalized sheaves on a smooth algebraic curve, which contains Stuhler's category of
generalized vector bundles or equivalently Seshadri's category of vector bundles with
parabolic structures. Furthermore, a cohomology theory for these generalized sheaves
analogous to the Zariski cohomology of coherent sheaves is discussed and used to
compute Ext-groups of generalized vector bundles. As an example, it is shown that the
Grothendieck decomposition theorem for vector bundles on $\mathbb P^1$ does not hold
for vector bundles with parabolic structures concentrated at three points.

Keywords: parabolic bundles, sheaf cohomology, Ext-groups