Pencils and critical locus on normal surfaces

2016/01/07 by F. Delgado, Delgado, F., Hélène Maugendre +2
Mathematics · #14B05 #14J17 #32S15 #32S45 #32S55 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.AG #msc:14B05 #msc:14J17 #msc:32S15 #msc:32S45 #msc:32S55

paper · pdf · doi:10.48550/arxiv.1601.01647

arxiv created 2016/01/07 · openalex publication_date 2016/01/07 · arxiv updated 2016/01/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study linear pencils of curves on normal surface singularities. Using the minimal good resolution of the pencil, we describe the topological type of generic elements of the pencil and characterize the behaviour of special elements. Then we show that the critical locus associated to the pencil is linked to the special elements. This gives a decomposition of the critical locus through the minimal good resolution and as a consequence, information on the topological type of the critical locus.

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