Smoothing singular extremal K\"ahler surfaces and minimal Lagrangians
Differential Geometry
2013-10-23 v3
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 K\"ahler classes. In addition, we construct small Lagrangian stationary spheres which represent Lagrangian vanishing cycles for surfaces close to the singular one.
Keywords
Cite
@article{arxiv.1211.6957,
title = {Smoothing singular extremal K\"ahler surfaces and minimal Lagrangians},
author = {Olivier Biquard and Yann Rollin},
journal= {arXiv preprint arXiv:1211.6957},
year = {2013}
}
Comments
Minor corrections