Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Genus three curves and 56 nodal sextic surfaces


Authors: Bert van Geemen and Yan Zhao
Journal: J. Algebraic Geom.
DOI: https://doi.org/10.1090/jag/694
Published electronically: March 30, 2018
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Abstract | References | Additional Information

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 such surfaces starting from non-hyperelliptic genus three curves. We illustrate our method by giving explicitly the equation of such a sextic surface starting from the Klein curve.


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Additional Information

Bert van Geemen
Affiliation: Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italia
Email: lambertus.vangeemen@unimi.it

Yan Zhao
Affiliation: Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italia; and Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, 2333CA Leiden, The Netherlands

DOI: https://doi.org/10.1090/jag/694
Received by editor(s): March 29, 2016
Received by editor(s) in revised form: June 20, 2016
Published electronically: March 30, 2018
Article copyright: © Copyright 2018 University Press, Inc.

American Mathematical Society