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Oberseminar WiSe 2011/12 Zusammenfassung des Vortrags von Michael Miesener

On the action of the automorphisms of the affine plane on semistable bundles

We consider the action of the group of automorphisms of the affine plane on semistable locally free sheaves on the projective plane which have rank 2, Chern classes ( 0,n ) and are trivial on a certain line.
We show that the jumping scheme of such a sheaf is reduced for n < 5. Using a lemma of Artamkin this shows that there are n -1 orbits for n < 5. Furthermore we see how one can extend the construction of Le Portier which we use for n = 4 to answer the question for n < 11 by investigating coherent systems supported on curves of degree 4.