This short paper concerns the existence of curves with low gonality on smooth hypersurfaces X in P^{n+1}. After reviewing a series of results on this topic, we report on a recent progress we achieved as a product of the Workshop Birational geometry of surfaces, held at University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained that if X is a very general hypersurface of degree d grater than or equal to 2n + 2, the least gonality of a curve C ⊂ X passing through a general point of X is explicitely given, apart from some exceptions we list.
Bastianelli, F., Ciliberto, C., Flamini, F., Supino, P. (2018). A note on gonality of curves on general hypersurfaces. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 11(1), 31-38 [10.1007/s40574-017-0129-x].
A note on gonality of curves on general hypersurfaces
CILIBERTO, CIROMembro del Collaboration Group
;FLAMINI, FLAMINIO
;
2018-04-03
Abstract
This short paper concerns the existence of curves with low gonality on smooth hypersurfaces X in P^{n+1}. After reviewing a series of results on this topic, we report on a recent progress we achieved as a product of the Workshop Birational geometry of surfaces, held at University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained that if X is a very general hypersurface of degree d grater than or equal to 2n + 2, the least gonality of a curve C ⊂ X passing through a general point of X is explicitely given, apart from some exceptions we list.| File | Dimensione | Formato | |
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