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Splitting types of semistable vector bundles on \(\mathbb P^2\). (English) Zbl 1254.14052

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)

Software:

SINGULAR; CoCoA
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