Volumes of line bundles as limits on generically nonreduced schemes. (English) Zbl 1511.14013

Núñez, Roberto

Rocky Mt. J. Math. 52, No. 6, 2129-2143 (2022).

Summary: 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.

MSC:

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

Keywords:

volume of line bundle; projective scheme

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