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| HAL: hal-00697614, version 1 |
| arXiv: 1205.3573 |
| DOI: 10.1007/s00208-013-0933-2 |
| Detailed view |  Export this paper |
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| Mathematische Annalen (2013) 37 pages |
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| Exemples de comptage de courbes sur les surfaces |
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| David Bourqui 1 |
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| (2013) |
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| Let X be a surface whose Cox ring has a single relation satisfying moreover a kind of linearity property. Under a simple assumption, we show that the geometric Manin's conjectures hold for some degrees lying in the dual of the effective cone of X (in particular, for those degrees the moduli space of morphisms has the expected dimension). The result applies to a class of generalized del Pezzo surfaces which has been intensively studied in the context of the arithmetic Manin's conjecture. |
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| 1: | 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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| Géométrie algébrique |
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| Subject | : | Mathematics/Algebraic Geometry Mathematics/Number Theory |
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| moduli spaces of morphisms of curves – Manin's conjecture – height zeta function – global field of positive characteristic – Cox rings – singular del Pezzo surfaces |
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| Attached file list to this document: | ||||||||||
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| hal-00697614, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00697614 | |
| oai:hal.archives-ouvertes.fr:hal-00697614 | |
| From: David Bourqui | |
| Submitted on: Tuesday, 15 May 2012 17:02:21 | |
| Updated on: Monday, 10 June 2013 16:11:30 | |
