Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic Chow polystability in K\"ahler geometry   It is conjectured that the existence of constant scalar curvature K\"ahler
metrics will be equivalent to K-stability, or K-polystability depending on
terminology (Yau-Tian-Donaldson conjecture).
  There is another GIT stability condition, called the asymptotic Chow
polystability.
  This condition implies the existence of balanced metrics for polarized
manifolds $(M, L^k)$ for all large $k$.
  It is expected that the balanced metrics converge to a constant scalar
curvature metric as $k$ tends to infinity under further suitable stability
conditions. In this survey article I will report on recent results saying that
the asymptotic Chow polystability does not hold for certain constant scalar
curvature K\"ahler manifolds. We also compare a paper of Ono with that of Della
Vedova and Zuddas.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an