Seiberg-Witten equations on surfaces of logarithmic general type

Details Seiberg-Witten equations on surfaces of logarithmic general type Seiberg-Witten equations on surfaces of logarithmic general type

2011-12-03

arxiv.org/abs/1112.0694v1

Mathematics

Differential Geometry

Scientific paper

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 Poincar\'e type metric at infinity. Then we compute a lower bound for the $L^{2}$-norm of scalar curvature on these spaces and give non-existence results for Einstein metrics on blow-ups.

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