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Finite-volume complex surfaces without cuspidal Einstein metrics

Abstract

We derive an obstruction to the existence of cuspidal Einstein metrics on finite-volume complex surfaces. This generalizes a theorem of LeBrun for compact complex surfaces. As in the compact case, such a result relies on a scalar curvature estimate. Finally, the obstruction is made explicit on some examples.

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Correspondence to Luca Fabrizio Di Cerbo.

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Di Cerbo, L.F. Finite-volume complex surfaces without cuspidal Einstein metrics. Ann Glob Anal Geom 41, 371–380 (2012). https://doi.org/10.1007/s10455-011-9289-6

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Keywords

  • Seiberg–Witten equations
  • Finite-volume Einstein metrics
  • Scalar curvature