On linear systems of \(\mathbb P^3\) through multiple points
type: Item
instance of: scholarly article
title: On linear systems of \(\mathbb P^3\) through multiple points
zbMATH Open document ID: 1113.14036
author: Cindy De Volder
author: Antonio Laface
published in: Journal of Algebra
publication date: 2007-04-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0311447
review text: Fix an integer \(d>0\), at most \(8\) general points of \(\mathbb {P}^3\) and consider the linear system \(M\) of all degree \(d\) surfaces with prescribed multiplicities at these points. Here the authors compute \(\dim (M)\) in the following way. They apply a space cubic Cremona transformation to transform \(M\) into another a similar problem \(N\) in standard form. They show that \(\dim (M)=\dim (N)\) and they give an explicit formula for \(\dim (N)\) in terms of the degree and the multiplicities needed to define \(N\).
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J30
zbMATH DE Number: 5144389
zbMATH Keywords: fat point
zbMATH Keywords: cubic Cremona transformation
zbMATH Keywords: linear systems
zbMATH Keywords: projective space
MaRDI profile type: Publication
OpenAlex ID: W2045009680
arXiv ID: math/0311447
cites work: Q5487004
cites work: Q3751693
cites work: Une conjecture pour la cohomologie des diviseurs sur les surfaces rationelles génériques.
cites work: On a class of special linear systems of $\mathbb{P}^3$
DOI: 10.1016/J.JALGEBRA.2006.12.003
description: scientific article