This paper concerns the existence of curves with low gonality on smooth hypersurfaces of sufficiently large degree. It has been recently proved that if X in IP^{n+1} is a hypersurface of degree d > n+1, and if C is an irreducible curve in X passing through a general point of X, then its gonality verifies gon(C) >= d-n, and equality is attained on some special hypersurfaces. Under the assumption of X a very general hypersurface of degree d >= 2n+2, we compute the least gonality c of an irreducible curve C in X passing through a general point of X apart from a series of possible exceptions, where the gonality may drop by one.

Bastianelli, F., Ciliberto, C., Flamini, F., Supino, P. (2019). Gonality of curves on general hypersurfaces. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 125, 94-118 [10.1016/j.matpur.2019.02.016].

Gonality of curves on general hypersurfaces

CILIBERTO, CIRO;FLAMINI, FLAMINIO;
2019

Abstract

This paper concerns the existence of curves with low gonality on smooth hypersurfaces of sufficiently large degree. It has been recently proved that if X in IP^{n+1} is a hypersurface of degree d > n+1, and if C is an irreducible curve in X passing through a general point of X, then its gonality verifies gon(C) >= d-n, and equality is attained on some special hypersurfaces. Under the assumption of X a very general hypersurface of degree d >= 2n+2, we compute the least gonality c of an irreducible curve C in X passing through a general point of X apart from a series of possible exceptions, where the gonality may drop by one.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - Geometria
English
Con Impact Factor ISI
Hypersurfaces; lines; gonality; vector bundles techniques
funds support from the research project Families of curves: their moduli and their related varieties, CUP: E81|18000100005" in the framework of the project Mission Sustainability
Bastianelli, F., Ciliberto, C., Flamini, F., Supino, P. (2019). Gonality of curves on general hypersurfaces. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 125, 94-118 [10.1016/j.matpur.2019.02.016].
Bastianelli, F; Ciliberto, C; Flamini, F; Supino, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/186774
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