The Donaldson–Futaki Invariant for Sequences of Test Configurations

  • Toshiki MabuchiEmail author
Part of the Progress in Mathematics book series (PM, volume 308)


In this paper, given a polarized algebraic manifold (X,L), we define the Donaldson–Futaki invariant \(F_1\left(\{\mu_{i}\}\right)\) for a sequence \(\{\mu_{i}\}\) of test configurations for (X,L) of exponents lisatisfying
$$l_i\rightarrow\;\infty,\quad \mathrm{as} \ j\rightarrow\;\infty.$$
This then allows us to define a strong version of K-stability or K-semistability for (X,L). In particular, (X,L) will be shown to be K-semistable in this strong sense if the polarization class \(c_1\left(L\right)_\mathbb{R}\) admits a constant scalar curvature Kähler metric.


Donaldson–Futaki invariants strong K-stability test configurations constant scalar curvature Kähler metrics. 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsOsaka UniversityToyonakaJapan

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