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 subsets of the archimedean points of projective flat schemes X over the ring of integers of a number field. This capacity can be used to generalize the converse part of the Fekete-Szeg\H{o} Theorem.
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Contributor : Laurent Moret-Bailly <>
Submitted on : Friday, January 27, 2012 - 11:30:40 AM
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Ted Chinburg, Laurent Moret-Bailly, Georgios Pappas, Martin Taylor. Finite Morphisms to Projective Space and Capacity Theory. journal für die reine und angewandte Mathematik (Crelles Journal), de Gruyter, 2017, 727, pp.69-84. ⟨⟩. ⟨10.1515/crelle-2014-0089⟩. ⟨hal-00663474⟩



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