An obstruction to asymptotic semistability and approximate critical metrics

2004/04/10 by Toshiki Mabuchi
Mathematics · #math.DG #math.AG #msc:32Q20

paper · pdf

published as Osaka J. Math. 41(2004), 463--472 · to appear in Osaka J. Math. 41(2004)

arxiv created 2004/04/10 · arxiv updated 2009/12/01

Abstract

In this paper, we consider an obstruction to asymptotic Chow-semistability of a polarized Kaehler algebraic manifold. Even when a linear algebraic group of positive dimension acts nontrivially and holomorphically on a polarized Kaehler algebraic manifold with constant scalar curvature, the vanishing of the obstruction allows us to generalize Donaldson's construction of approximate solutions for equations of balanced metrics.

Related

• Asymptotic Chow polystability in Kähler geometry
• Asymptotic polybalanced kernels on extremal Kaehler manifolds
• The Donaldson-Futaki invariant for sequences of test configurations
• Logarithmic Chow semistability of polarized toric manifolds
• The Yau-Tian-Donaldson Conjecture for general polarizations