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arXiv · 2009.08249

Volumes of line bundles as limits on generically nonreduced schemes

Roberto Nunez
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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.

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Roberto Nunez. 2020-09-15. Volumes of line bundles as limits on generically nonreduced schemes. https://arxiv.org/abs/2009.08249

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