Title: On subfiniteness of graded linear series,
Abstract: Hilbert's 14th problem studies the finite generation property of the
intersection of an integral algebra of finite type with a subfield of the field
of fractions of the algebra. It has a negative answer due to the counterexample
of Nagata. We show that a subfinite version of Hilbert's 14th problem has a
confirmative answer. We then establish a graded analogue of this result, which
permits to show that the subfiniteness of graded linear series does not depend
on the function field in which we consider it. Finally, we apply the
subfiniteness result to the study of geometric and arithmetic graded linear
series.