We consider the problem of existence of constant scalar curvature Kähler 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 Kähler-Einstein metric, and a strong evidence of K-stability of complete intersections in Grassmannians.

Arezzo, C., DELLA VEDOVA, A. (2011). On the K-stability of complete intersections in polarized manifolds. ADVANCES IN MATHEMATICS, 226(6), 4796-4815 [10.1016/j.aim.2010.12.018].

On the K-stability of complete intersections in polarized manifolds

DELLA VEDOVA, ALBERTO
2011

Abstract

We consider the problem of existence of constant scalar curvature Kähler 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 Kähler-Einstein metric, and a strong evidence of K-stability of complete intersections in Grassmannians.
Articolo in rivista - Articolo scientifico
Complete intersection; Constant scalar curvature Kähler metric; Fano manifold; Futaki invariant; K-stability; Kähler-Einstein metric; Mathematics (all)
English
2011
226
6
4796
4815
none
Arezzo, C., DELLA VEDOVA, A. (2011). On the K-stability of complete intersections in polarized manifolds. ADVANCES IN MATHEMATICS, 226(6), 4796-4815 [10.1016/j.aim.2010.12.018].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/56498
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