Chebyshev potentials, Fubini–Study metrics, and geometry of the space of Kähler metrics
Chenzi Jin,
Yanir A. Rubinstein
Abstract:The Chebyshev potential of a Hermitian metric on an ample line bundle over a projective variety, introduced by Witt Nyström, is a convex function defined on the Okounkov body. It is a generalization of the symplectic potential of a torus‐invariant Kähler potential on a toric variety, introduced by Guillemin, that is a convex function on the Delzant polytope. A folklore conjecture asserts that a curve of Chebyshev potentials associated to a subgeodesic in the space of positively curved Hermitian metrics is line… Show more
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