Degré des diviseurs sur les familles de courbes de \({\mathbb{P}}^ 3\). (Degree of divisors on families of curves of \({\mathbb{P}}^ 3)\)
type: Item
instance of: scholarly article
title: Degré des diviseurs sur les familles de courbes de \({\mathbb{P}}^ 3\). (Degree of divisors on families of curves of \({\mathbb{P}}^ 3)\)
zbMATH Open document ID: 0612.14026
DOI: 10.1007/BF01473440
author: Nicole Mestrano
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/182972
review text: Let \(U_{d,g}\to H_{d,g}\) be the universal family of connected smooth curves of \({\mathbb{P}}^ 3\) of genus \(g\) and degree \(d.\) The relative tangent bundle and the hyperplane divisor of \({\mathbb{P}}^ 3\) define on \(U_{d,g}^ a \)divisor whose (relative) degree is \(\delta =g.c.d.(2g- 2,d)\). Assume \(d\geq \frac{5}{4}g+1\), so that \(H_{d,g}\) is connected. The author proves that if d is large enough with respect to g, then the degree of every divisor on \(U_{d,g}\) is a multiple of \(\delta\). This result provides an analog for \({\mathbb{P}}^ 3\) to a theorem of Enriques and Chisini stating, in modern terms, that on the universal family of curves of \({\mathbb{P}}^{g-1}\) of genus \(g\geq 3\) and degree \(2g-2\) every divisor has degree multiple of 2g-2.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 3989531
zbMATH Keywords: degree of divisor
zbMATH Keywords: projective space curve
zbMATH Keywords: universal family of curves
reviewed by: Antonio Lanteri
MaRDI profile type: Publication
cites work: Q4750779
cites work: Q3689280
cites work: Q3693625
description: scientific article; zbMATH DE number 3989531