On the K-stability of complete intersections in polarized manifolds

Details On the K-stability of complete intersections in polarized manifolds On the K-stability of complete intersections in polarized manifolds

2008-10-08

arxiv.org/abs/0810.1473v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

We consider the problem of existence of constant scalar curvature Kaehler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the ambient manifold. As applications we give a new Mukai-Umemura-Tian like example of Fano 5-fold admitting no Kaehler-Einstein metric and a strong evidence of K-stability of complete intersections on Grassmannians.

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