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.
Genus three curves and 56 nodal sextic surfaces / B. Van Geemen, Y. Zhao. - In: JOURNAL OF ALGEBRAIC GEOMETRY. - ISSN 1056-3911. - 27:4(2018), pp. 583-592.
Genus three curves and 56 nodal sextic surfaces
B. Van Geemen;
2018
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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