2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60791We 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.43 pages; in this new version, a mistake has been corrected and hence the original classification of the Main Theorem has been slightly modifiedDifferential Geometry53C55, 53C25, 57S15text