Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex plurisubharmonic geodesics via the generalized Legendre
  transform to the Okounkov body   Consider a complex projective manifold X together with an ample line bundle
L. In previous work, Witt Nystr\"om defined a generalized Legendre transform
(or Chebyshev transform), sending a continuous psh metric on L to a convex
function on the Okounkov body (a generalized moment polytope). We show that a
psh segment on L is geodesic if and only its associated segment of Chebyshev
transforms is affine, hereby generalizing the corresponding statement in toric
geometry. We then look into the maximal geodesic rays of
Berman-Boucksom-Jonsson, which we characterize completely as having their
associated ray of transforms be affine, and their collection of slopes at
infinity correspond with the Chebyshev transform (in the sense of
Boucksom-Chen-Maclean) of the associated non-Archimedean metric on the
Berkovich analytification of L with respect to the trivial absolute value on C.
This can be interpreted as saying that along such rays, the non-Archimedean
Chebyshev transform is the degenerated (hybrid) limit of the complex Chebyshev
transforms.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph