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Abstract des Vortrages von Thomas Szemberg

Bounded negativity and arrangements of lines

This talk is based on the recent preprint arXiv:1407.2966 with Thomas Bauer, Sandra Di Rocco, Brian Harbourne, Jack Huizenga, Anders Lundman and Piotr Pokora. The bounded negativity conjecture (BNC) predicts that on a given surface S, there is a lower bound on the self-intersection of reduced curves C on S. So far it is not even known if this property is birational invariant. I will discuss BNC on certain blow ups of the projective plane.