Running after a new Kaehler-Einstein metric
微分几何
2007-05-23 v2
摘要
We deal with compact Kaehler manifolds M which are acted on by a semisimple compact Lie group G of isometries with codimension one regular orbits. We provide an explicit description of the standard blow-ups of such manifolds along complex singular orbits, in case b_1(M) = 0 and the regular orbits are Levi nondegenerate. Up to very few exceptions, all the nonhomogeneous manifolds in this class are shown to admit a G-invariant Kaehler-Einstein metric, giving completely new examples of compact Kaehler-Einstein manifolds.
引用
@article{arxiv.math/0101173,
title = {Running after a new Kaehler-Einstein metric},
author = {Fabio Podesta' and Andrea Spiro},
journal= {arXiv preprint arXiv:math/0101173},
year = {2007}
}
备注
43 pages; in this new version, a mistake has been corrected and hence the original classification of the Main Theorem has been slightly modified