Finite Morphisms to Projective Space and Capacity Theory
Abstract
We study conditions on a commutative ring R which are equivalent to the following requirement; whenever X is a projective scheme over S = Spec(R) of fiber dimension \leq d for some integer d \geq 0, there is a finite morphism from X to P^d_S over S such that the pullbacks of coordinate hyperplanes give prescribed subschemes of X provided these subschemes satisfy certain natural conditions. We use our results to define a new kind of capacity for adelic subsets of projective schemes X over global fields. This capacity can be used to generalize the converse part of the Fekete-Szeg\H{o} Theorem.
Cite
@article{arxiv.1201.0678,
title = {Finite Morphisms to Projective Space and Capacity Theory},
author = {Ted Chinburg and Laurent Moret-Bailly and Georgios Pappas and Martin Taylor},
journal= {arXiv preprint arXiv:1201.0678},
year = {2012}
}
Comments
16 pages, major revision following referee's report. In particular, the finite morphism capacity has been redefined and is now compared with the sectional capacity