Genus three curves and 56 nodal sextic surfaces

2016/03/20 by Bert van Geemen, Yan Zhao, van Geemen, Bert +1 · 1 citation
Mathematics · #14J25 #14Q10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1603.06247

openalex publication_date 2016/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Catanese and Tonoli showed that the maximal cardinality for an even set of nodes on a sextic surface is 56 and they constructed such nodal surfaces. In this paper we give an alternative, rather simple, construction for these surfaces starting from a non-hyperelliptic genus three curve. We illustrate our method by giving explicitly the equation of such a sextic surface starting from the Klein curve.

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