descriptionPublicationkeyboard_double_arrow_right Article , Preprint 12 Sep 2022Embargo end date: 01 Jan 2020 English Publisher:Cellule MathDoc/Centre MersenneJournal:Annales de l'Institut Fourier, volume 72, pages 1,329-1,377 (eissn: 1777-5310,

Authors: Gualdi, Roberto; Martínez, César;

doi: 10.5802/aif.3500 , 10.48550/arxiv.2001.11468

arXiv: http://arxiv.org/abs/2001.11468

handle: 2117/405818

Higher dimensional essential minima and equidistribution of cycles

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Abstract

The essential minimum and equidistribution of small points are two well-established interrelated subjects in arithmetic geometry. However, there is lack of an analogue of essential minimum dealing with higher dimensional subvarieties, and the equidistribution of these is a far less explored topic.In this paper, we introduce a new notion of higher dimensional essential minimum and use it to prove equidistribution of generic and small effective cycles. The latter generalizes the previous higher dimensional equidistribution theorems by considering cycles and by allowing more flexibility on the arithmetic datum.

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Keywords

Equidistribution of cycles, Essential minimum, Heights, Geometry, Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), Diophantine geometry, Algebraic, Mathematics - Algebraic Geometry, FOS: Mathematics, Arakelov geometry, Geometria algèbrica, Number Theory (math.NT), Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica, Algebraic Geometry (math.AG), Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry, Mathematics - Number Theory, 14G40, 11G35, 14C25, Geometry, Algebraic, Geometria algèbrica--Aritmètica, Arithmetical algebraic geometry, Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres, Anàlisi diofàntica

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