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Oberseminar WiSe 12/13 Zusammenfassung des Vortrags von Pawel Sosna

Construction of (quasi-)phantom categories on some surfaces of general type

I will report on the construction of non-full exceptional collections of maximal length 11 on the Barlow and the classical Godeaux surface. The (left or right) orthogonal complement of such a collection gives an example of a category with trivial Hochschild homology and trivial (Barlow case) respectively torsion (Godeaux case) Grothendieck group. The former is called a phantom and the latter a quasi-phantom. This is joint work with Christian Böhning, Hans-Christian Graf von Bothmer and Ludmil Katzarkov.