On the stability of the restricted bundle of space curves contained in a quartic surface
type: Item
instance of: scholarly article
title: On the stability of the restricted bundle of space curves contained in a quartic surface
zbMATH Open document ID: 0901.14018
published in: Beiträge zur Algebra und Geometrie
publication date: 1998-11-26T00:00:00Z
full work available at URL: https://eudml.org/doc/231600
full work available at URL: no.2
review text: The author shows that, for \((d+13)^2/9\leq g<(d-1)^2/8\), there exist smooth connected curves \(Z\) in \(\mathbb{P}^3\), of degree \(d\) and genus \(g\), such that the restriction of the tangent bundle of \(\mathbb{P}^3\) to \(Z\) is stable. The main ingredients in his proof are a definition of stability for vector bundles on reduced but not necessarily irreducible curves due to \textit{G. Hein} and \textit{H. Kurke} [in: Proc. Hirzeburch 65 Conf. Algebraic Geometry, Ramat Gan 1993, Isr. Math. Conf. Proc. 9, 283-294 (1996; Zbl 0859.14011)] and a construction of \textit{L. Gruson} and \textit{C. Peskine} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 15, 401-418 (1982; Zbl 0517.14007)] of smooth space curves on a rational quartic surface with a double line in \(\mathbb{P}^3\). The author also proves similar results for curves in \(\mathbb{P}^n\), \(n=3,4,5\), with simple restricted tangent bundle.
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14H60
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 1066110
zbMATH Keywords: space curve
zbMATH Keywords: stable tangent bundle
author: E. Ballico
reviewed by: Iustin Coandă
MaRDI profile type: Publication
Recommended article: Stable rationality of quadric and cubic surface bundle fourfolds
Recommended article: Stable rationality of quadric surface bundles over surfaces
Recommended article: Stable vector bundles on quadric hypersurfaces
Recommended article: Quadric surface bundles over surfaces and stable rationality
Recommended article: On moduli spaces for stable bundles on quadrics
Recommended article: Stability of quadric bundles
Recommended article: Stability of Kapranov bundles on quadrics
Recommended article: On the rationality of quadric surface bundles
Recommended article: A refined stable restriction theorem for vector bundles on quadric threefolds
Recommended article: About the stability of the tangent bundle restricted to a curve
description: scientific article; zbMATH DE number 1066110