6533b7dbfe1ef96bd127141a

RESEARCH PRODUCT

On the K-stability of complete intersections in polarized manifolds

Claudio ArezzoClaudio ArezzoAlberto Della VedovaAlberto Della Vedova

subject

Kähler–Einstein metricMathematics - Differential GeometryPure mathematicsMathematics(all)General MathematicsComplete intersectionVector bundleFano plane01 natural sciencesMathematics - Algebraic GeometryKähler–Einstein metricKähler-Einstein metricMathematics::Algebraic Geometry0103 physical sciencesFOS: MathematicsMathematics (all)0101 mathematicsInvariant (mathematics)Algebraic Geometry (math.AG)Complete intersectionMathematics::Symplectic GeometryMathematics010308 nuclear & particles physics010102 general mathematicsMathematical analysisK-stabilityManifoldDifferential Geometry (math.DG)Futaki invariant53C55 14J99Constant scalar curvature Kähler metricMathematics::Differential GeometryFano manifoldScalar curvature

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.

yearjournalcountryeditionlanguage
2011-04-01
10.1016/j.aim.2010.12.018http://arxiv.org/abs/0810.1473