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
Van Geemen, Bert;
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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
1603.06247.pdf
accesso aperto |
133.45 kB | Adobe PDF | Visualizza/Apri |
|
S1056-3911-2018-00694-0.pdf
non disponibili |
174.23 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
Caricamento pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
