Volumes of line bundles as limits on generically nonreduced schemes
Algebraic Geometry
2021-02-11 v2
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.
Keywords
Cite
@article{arxiv.2009.08249,
title = {Volumes of line bundles as limits on generically nonreduced schemes},
author = {Roberto Nunez},
journal= {arXiv preprint arXiv:2009.08249},
year = {2021}
}
Comments
21 pages. arXiv admin note: text overlap with arXiv:2007.12925