Farnik, Michał; Stäbler, Axel Splitting types of semistable vector bundles on \(\mathbb P^2\). (English) Zbl 1254.14052 Matematiche 64, No. 2, 91-98 (2009). Summary: We show that for \(n\leq 5\) all generic splitting types of semistable vector bundles of rank \(n\) on \(\mathbb P^2\) on which are in principle possible by the theorem of Grauert-Mülich actually occur. We prove this by constructing examples for all possible splitting types. MSC: 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli 14-04 Software, source code, etc. for problems pertaining to algebraic geometry 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) Keywords:splitting types; semistable vector bundles Software:SINGULAR; CoCoA PDFBibTeX XMLCite \textit{M. Farnik} and \textit{A. Stäbler}, Matematiche 64, No. 2, 91--98 (2009; Zbl 1254.14052) Full Text: Link