Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Basis divisors and balanced metrics   Using log canonical thresholds and basis divisors Fujita--Odaka introduced
purely algebro-geometric invariants $\delta_m$ whose limit in $m$ is now known
to characterize uniform K-stability on a Fano variety. As shown by Blum-Jonsson
this carries over to a general polarization, and together with work of Berman,
Boucksom, and Jonsson, it is now known that the limit of these
$\delta_m$-invariants characterizes uniform Ding stability. A basic question
since Fujita-Odaka's work has been to find an analytic interpretation of these
invariants. We show that each $\delta_m$ is the coercivity threshold of a
quantized Ding functional on the $m$-th Bergman space and thus characterizes
the existence of balanced metrics. This approach has a number of applications.
The most basic one is that it provides an alternative way to compute these
invariants, which is new even for $\mathbb{P}^n$. Second, it allows us to
introduce algebraically defined invariants that characterize the existence of
K\"ahler-Ricci solitons (and the more general $g$-solitons of Berman-Witt
Nystr\"om), as well as coupled versions thereof. Third, it leads to
approximation results involving balanced metrics in the presence of
automorphisms that extend some results of Donaldson.

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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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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: patt-sol
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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: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: q-bio