Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tits buildings and K-stability   A polarized variety is K-stable if, for any test configuration, the
Donaldson-Futaki invariant is positive. In this paper, inspired by classical
geometric invariant theory, we describe the space of test configurations as a
limit of a direct system of Tits buildings. We show that the Donaldson-Futaki
invariant, conveniently normalized, is a continuous function on this space. We
also introduce a pseudo-metric on the space of test configurations. Recall that
K-stability can be enhanced by requiring that the Donaldson-Futaki invariant is
positive on any admissible filtration of the co-ordinate ring. We show that
admissible filtrations give rise to Cauchy sequences of test configurations
with respect to the above mentioned pseudo-metric.

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The categories of this paper are: math-ph
31
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: bayes-an
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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: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph