Concave transforms of filtrations and rationality of Seshadri constants

Autor:	Küronya, Alex, Maclean, Catriona, Roé, Joaquim
Rok vydání:	2019
Předmět:	Mathematics - Algebraic Geometry Mathematics - Commutative Algebra Mathematics - Complex Variables 14C20 13D40 32Q15 52A99
Druh dokumentu:	Working Paper
Popis:	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. Comment: 32 pages. Improved exposition, simplified some proofs. Comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1901.00384 Zobrazit plný text záznamu View this record from Arxiv