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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Bibliographic Details
Published in:arXiv.org 2008-10
Main Authors: Arezzo, Claudio, Alberto Della Vedova
Format: Article
Language:English
Subjects:
Curvature
Intersections
Invariants
Manifolds
Stability
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0810.1473