Concave transforms of filtrations and rationality of Seshadri constants
Algebraic Geometry
2019-03-28 v2 Commutative Algebra
Complex Variables
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. Along the way we introduce Newton--Okounkov bodies of abstract graded semigroups and determine conditions for their slices to be Newton--Okounkov bodies of subsemigroups.
Keywords
Cite
@article{arxiv.1901.00384,
title = {Concave transforms of filtrations and rationality of Seshadri constants},
author = {Alex Küronya and Catriona Maclean and Joaquim Roé},
journal= {arXiv preprint arXiv:1901.00384},
year = {2019}
}
Comments
32 pages. Improved exposition, simplified some proofs. Comments are welcome