This paper concerns the existence of curves with low gonality on smooth hypersurfaces of sufficiently large degree. It has been recently proved that if $X subset P^{n+1}$ is a hypersurface of degree $dgeq n+2$, and if $Csubset X$ is an irreducible curve passing through a general point of $X$, then its gonality verifies $ gon(C) geq d-n$, and equality is attained on some special hypersurfaces. We prove that if $X subset P^{n+1}$ is a very general hypersurface of degree $dgeq 2n+2$, the least gonality of an irreducible curve $Csubset X$ passing through a general point of $X$ is $ gon(C) = d-leftlfloor ( sqrt{16n+1}-1)/2 ightfloor $, apart from a series of possible exceptions, where $gon(C)$ may drop by one.

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

Gonality of curves on general hypersufaces

Paola Supino
2019-01-01

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 $X subset P^{n+1}$ is a hypersurface of degree $dgeq n+2$, and if $Csubset X$ is an irreducible curve passing through a general point of $X$, then its gonality verifies $ gon(C) geq d-n$, and equality is attained on some special hypersurfaces. We prove that if $X subset P^{n+1}$ is a very general hypersurface of degree $dgeq 2n+2$, the least gonality of an irreducible curve $Csubset X$ passing through a general point of $X$ is $ gon(C) = d-leftlfloor ( sqrt{16n+1}-1)/2 ightfloor $, apart from a series of possible exceptions, where $gon(C)$ may drop by one.
2019
Bastianelli, F., Ciliberto, C., Flamini, F., Supino, P. (2019). Gonality of curves on general hypersufaces. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 125, 94-118 [10.1016/j.matpur.2019.02.016].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/340678
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