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arXiv · 1211.6957

Smoothing singular extremal Kähler surfaces and minimal Lagrangians

Olivier Biquard·Yann Rollin
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Abstract

We consider smoothings of a complex surface with singularities of class T and no nontrivial holomorphic vector field. Under an hypothesis of non degeneracy of the smoothing at each singular point, we prove that if the singular surface admits an extremal metric, then the smoothings also admit extremal metrics in nearby Kähler classes. In addition, we construct small Lagrangian stationary spheres which represent Lagrangian vanishing cycles for surfaces close to the singular one.

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Olivier Biquard, Yann Rollin. 2013-10-22. Smoothing singular extremal Kähler surfaces and minimal Lagrangians. https://arxiv.org/abs/1211.6957

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