Volumes of line bundles as limits on generically nonreduced schemes

DOI10.1216/RMJ.2022.52.2129arXiv2009.08249MaRDI QIDQ6349311

Publication date: 15 September 2020

Abstract: The volume of a line bundle is defined in terms of a limsup. It is a fundamental question whether this limsup is a limit. It has been shown that this is always the case on generically reduced schemes. We show that volumes are limits in two classes of schemes that are not necessarily generically reduced: codimension one subschemes of projective varieties such that their components of maximal dimension contain normal points and projective schemes whose nilradical squared equals zero.

Mathematics Subject Classification ID

Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Riemann-Roch theorems (14C40)

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