On the K-stability of complete intersections in polarized manifolds

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...

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Published in:arXiv.org 2008-10
Main Authors: Arezzo, Claudio, Alberto Della Vedova
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Language:English
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Curvature
Intersections
Invariants
Manifolds
Stability
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Alberto Della Vedova
description 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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subjects Curvature
Intersections
Invariants
Manifolds
Stability
title On the K-stability of complete intersections in polarized manifolds
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