The volume of a line bundle is an invariant defined in terms of a limit superior.
It is a fundamental question whether this limit superior is a limit. It has been
shown that this is always the case on generically reduced proper schemes over
arbitrary fields. 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.
Meeting ID: 968 4560 7004