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Published in:
2015 | OriginalPaper | Chapter
The Donaldson–Futaki Invariant for Sequences of Test Configurations
Published in: Geometry and Analysis on Manifolds
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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 l
i
satisfying
$$l_i\rightarrow\;\infty,\quad \mathrm{as} \ j\rightarrow\;\infty.$$
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.