Gonality and Clifford index of curves on elliptic K3 surfaces with Picard number two

Ramponi, M.

doi:10.1007/s00013-016-0879-1

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Moreover Curves Cut Out On X By Tri-tangent Planes (And Only...1

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2017

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“…For all admissible cases, a family of expected dimension of nodal curves in |O X (1)| with geometric genus g, carrying a g 1 k on their normalizations, has been exhibited. Similar problems have been investigated in different settings, for instance on rational and ruled surfaces [3,10,37,48], Enriques surfaces [31,32], elliptic K3's [46], toric surfaces [29], as well as abelian ones [30,44].…”

Section: Moreover Curves Cut Out On X By Tri-tangent Planes (And Only...mentioning

confidence: 99%

A note on gonality of curves on general hypersurfaces

Bastianelli

Ciliberto

Flamini

et al. 2017

Boll Unione Mat Ital

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This short paper concerns the existence of curves with low gonality on smooth\ud hypersurfaces X in P^{n+1}. After reviewing a series of results on this topic, we report on a recent\ud progress we achieved as a product of the Workshop Birational geometry of surfaces, held at\ud University of Rome “Tor Vergata” on January 11th–15th, 2016. In particular, we obtained\ud that if X is a very general hypersurface of degree d grater than or equal to 2n + 2, the least gonality of\ud a curve C ⊂ X passing through a general point of X is explicitely given, apart\ud from some exceptions we list

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