Concave transforms of filtrations and rationality of Seshadri constants

Küronya, Alex; Maclean, Catriona; Roé, Joaquim

doi:10.1090/tran/8345

Concave transforms of filtrations and rationality of Seshadri constants
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Abstract:

We show that the subgraph of the concave transform of a multiplicative filtration on a section ring is the Newton–Okounkov body of a certain semigroup, and if the filtration is induced by a divisorial valuation, then the associated graded algebra is the algebra of sections of a concrete line bundle in higher dimension. We use this description to give a rationality criterion for certain Seshadri constants.

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