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Oberseminar SoSe 2010 Zusammenfassung des Vortrags von H. Hartmann (Bonn)

Stability conditions on K3 surfaces near cusps of the Kaehler moduli space

Recently Shouhei Ma discovered a bijection between cusps of the (Baily-Borel compactification) of the Kaehler moduli space associated to a K3 surface X and the set of Fourier-Mukai partners of X, i.e. K3 surfaces X' having an equivalent derived category. His proof relies on a deep theorem due to Mukai and Orlov which reduces this statement to lattice theory. We will explain some more geometric statements motivated by Ma's theorem using Bridgeland stability conditions on X.