Seiberg-Witten equations on surfaces of logarithmic general type

2011/12/03 by Luca Di Cerbo, Di Cerbo, Luca
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.1112.0694

arxiv created 2011/12/03 · arxiv updated 2011/12/06

Abstract

We study the Seiberg-Witten equations on surfaces of logarithmic general type. First, we show how to construct irreducible solutions of the Seiberg-Witten equations for any metric which is "asymptotic" to a Poincaré type metric at infinity. Then we compute a lower bound for the L²-norm of scalar curvature on these spaces and give non-existence results for Einstein metrics on blow-ups.

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