arXiv subjects
Publications and source records attributed to Roberto Nunez.
Volumes of line bundles are known to exist as limits on generically reduced projective schemes. However, it is not known if they always exist as limits on more general projective schemes. We show that they do always exist as a limit on a codimension one subscheme of a nonsingular projective variety.
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.