Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform stability of twisted constant scalar curvature K\"ahler metrics   We introduce a norm on the space of test configurations, which we call the
minimum norm. We conjecture that uniform K-stability with respect to this norm
is equivalent to the existence of a constant scalar curvature K\"ahler metric.
This notion of uniform K-stability is analogous to coercivity of the Mabuchi
functional. We characterise the triviality of test configurations, by showing
that a test configuration has zero minimum norm if and only if it has zero
$L^2$-norm, if and only if it is almost trivial.
  We prove that the existence of a twisted constant scalar curvature K\"ahler
metric implies uniform twisted K-stability with respect to the minimum norm,
when the twisting is ample.
  We give algebro-geometric proofs of uniform K-stability in the general type
and Calabi-Yau cases, as well as in the Fano case under an alpha invariant
condition. Our results hold for line bundles sufficiently close to the
(anti)-canonical line bundle, and also in the twisted setting. We show that log
K-stability implies twisted K-stability, and also that twisted K-semistability
of a variety implies that the variety has mild singularities.

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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: stat