descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 May 2016Embargo end date: 01 Jan 2015 English Publisher:Elsevier BVJournal:Journal de Mathématiques Pures et Appliquées, volume 105, pages 734-743 (issn: 0021-7824,

Authors: Barja, Miguel Ángel; PARDINI, RITA; Stoppino, Lidia;

doi: 10.1016/j.matpur.2015.11.012 , 10.48550/arxiv.1504.06590

arXiv: http://arxiv.org/abs/1504.06590

handle: 2117/103930 , 11568/825245 , 11571/1277146

Surfaces on the Severi line

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Abstract

Let S be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has $K^2_S\geq 4χ(\mathcal O_S)$. We prove that the equality $K^2_S=4χ(\mathcal O_S)$ holds if and only if $q(S):= h^1(\mathcal O_S)=2$ and the canonical model of $S$ is a double cover of the Albanese surface branched on an ample divisor with at most negligible singularities.

13 pages

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
University of Pisa
Italy
Universitat Politècnica de Catalunya
Spain
University of Pavia
Italy
University of Insubria
Italy

Keywords

inequality, Linear systems, :14 Algebraic geometry::14J Surfaces and higher-dimensional varieties [Classificació AMS], 510, Irregular varieties; Severi inequality; Surfaces of general type; Étale coverings; Applied Mathematics; Mathematics (all), Mathematics - Algebraic Geometry, Severi inequality, FOS: Mathematics, :14 Algebraic geometry::14E Birational geometry [Classificació AMS], 14J29, Algebraic Geometry (math.AG), Classificació AMS::14 Algebraic geometry::14J Surfaces and higher-dimensional varieties, Surfaces of general type, Àrees temàtiques de la UPC::Matemàtiques i estadística, Irregular varieties, :14 Algebraic geometry::14C Cycles and subschemes [Classificació AMS], general type, :Matemàtiques i estadística [Àrees temàtiques de la UPC], Classificació AMS::14 Algebraic geometry::14E Birational geometry, Topologia algebraica, 14C20, 14E20, varieties, Sistemes lineals, Etale coverings, Étale coverings, Irregular varietie, Classificació AMS::14 Algebraic geometry::14C Cycles and subschemes, Algebraic topology

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