Non-minimal scalar-flat Kaehler surfaces and parabolic stability
Differential Geometry
2007-05-23 v5 Algebraic Geometry
Abstract
A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable holomorphic bundles. This rather general construction is shown also to give new examples of low genus: in particular, it is shown that CP^2 blown up at 10 suitably chosen points, admits a scalar-flat Kaehler metric; this answers a question raised by Claude LeBrun in 1986 in connection with the classification of compact self-dual 4-manifolds.
Cite
@article{arxiv.math/0404423,
title = {Non-minimal scalar-flat Kaehler surfaces and parabolic stability},
author = {Yann Rollin and Michael A. Singer},
journal= {arXiv preprint arXiv:math/0404423},
year = {2007}
}
Comments
Final version, 30 pages, the appendix has been suppressed and will appear elsewhere, to be published in Inventiones Mathematicae