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| HAL: hal-00663474, version 1 |
| arXiv: 1201.0678 |
| Detailed view |  Export this paper |
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| Finite Morphisms to Projective Space and Capacity Theory |
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| Ted Chinburg 1Laurent Moret-Bailly 2 |
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| (2012-01-03) |
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| 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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| 1: | Department of Mathematics, University of Pennsylvania |
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University of Pennsylvania |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3: | Department of Mathematics, Michigan State University |
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Michigan State University |
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| 4: | Mathematical Institute [Oxford] (MI) |
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University of Oxford |
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| Géométrie algébrique |
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| Subject | : | Mathematics/Algebraic Geometry Mathematics/Number Theory |
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| finite morphism – Picard group – varieties over global fields – capacity theory |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1201.0678 |
| hal-00663474, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00663474 | |
| oai:hal.archives-ouvertes.fr:hal-00663474 | |
| From: Laurent Moret-Bailly | |
| Submitted on: Friday, 27 January 2012 11:30:40 | |
| Updated on: Monday, 30 January 2012 16:34:28 | |
