

Iskovskikh Seminar
October 31, 2013 18:00, Moscow, Steklov Mathematical Institute, room 540






Vector bundles of rank 2 and linear systems on algebraic surfaces (following the paper of I. Reider)
N. A. Pechenkin^{} ^{} Steklov Mathematical Institute of the Russian Academy of Sciences

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Abstract:
We will prove the technical theorem about linear systems of the form $K+L$ (where $K$ is the canonical divisor and $L$ is a numerical effective divisor) on smooth algebraic surfaces. The proof will be based on the notion of Bogomolov's instability of rank 2 vector bundles. As a consequence of the theorem, we will get easy proofs for some quite deep results on the geometry of surfaces.

