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Genus three curves and 56 nodal sextic surfaces

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.

preprint2016arXivOpen access
Bert van GeemenYan Zhao
math.AG
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Bert van GeemenYan Zhao

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