On regular ruled surfaces in \({\mathbb{P}}^ 3\)
type: Item
instance of: scholarly article
title: On regular ruled surfaces in \({\mathbb{P}}^ 3\)
zbMATH Open document ID: 0686.14044
DOI: 10.1007/BF01277069
author: Manuel Pedreira
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: In the author's joint paper with \textit{E. Arrondo} and \textit{I. Sols} [Algebraic curves and projective geometry, Proc. Conf., Trento/Italy 1988, Lect. Notes Math. 1389, 1-15 (1989)] appears a proof in nowaday's terms, of \textit{F. Severi}'s assertion [Rend. Mat., Univ. Roma, V. Ser. 2, 1-32 (1941; Zbl 0024.34301)] that there are regular ruled surfaces of degree \( d\) and \(irregularity\quad q,\) if and only if \(d\geq 2q+2\), and the corresponding Hilbert scheme is irreducible and of general moduli. We can thus talk about the generic ruled surface of degree \( d\) and \(irregularity\quad q.\) The main purpose of this paper is to prove a maximal rank theorem for regular ruled surfaces in \({\mathbb{P}}^ 3\) by using these results. This fact was taken for granted by the Italian geometers as a ``principio de enumerazione delle constanti'', but an effective proof of it wasn't known in the literature up to now.
Mathematics Subject Classification ID: 14J26
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 4123900
zbMATH Keywords: generic ruled surface
zbMATH Keywords: degree
zbMATH Keywords: irregularity
zbMATH Keywords: maximal rank theorem
MaRDI profile type: Publication
cites work: The maximal rank conjecture for non special curves in \({\mathbb{P}}^ 3\)
cites work: Q3218233
full work available at URL: https://doi.org/10.1007/bf01277069
OpenAlex ID: W2071747172
description: scientific article; zbMATH DE number 4123900