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;
2019-01-04

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.
4-gen-2019
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
Articolo su rivista
File in questo prodotto:
File Dimensione Formato  
JMPA2019Pubb.pdf

solo utenti autorizzati

Descrizione: Articolo principale
Tipologia: Versione Editoriale (PDF)
Licenza: Copyright dell'editore
Dimensione 576.04 kB
Formato Adobe PDF
576.04 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/186774
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 6
social impact