Running after a new Kaehler-Einstein metric

Details Running after a new Kaehler-Einstein metric Running after a new Kaehler-Einstein metric

2001-01-21

arxiv.org/abs/math/0101173v2

Mathematics

Differential Geometry

43 pages; in this new version, a mistake has been corrected and hence the original classification of the Main Theorem has been

Scientific paper

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.

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