Elementary (-1)-curves of P³

2006/05/03 by Antonio Laface, Laface, Antonio, Luca Ugaglia +1
Engineering · Mathematics · #14C20 #Advanced Differential Equations and Dynamical Systems #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #math.AG #msc:14C20

paper · pdf · doi:10.48550/arxiv.math/0605106

12 pages, LaTeX

arxiv created 2006/05/03 · openalex publication_date 2006/05/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we deal with rational curves in P³ which are images of a line by means of a finite sequence of cubo-cubic Cremona transformations. We prove that these curves can always be obtained applying to the line a sequence of such transformations increasing at each step the degree of the curve. As a corollary we get a result about curves that can give speciality for linear systems of P³.

Related

• A conjecture on special linear systems of P³
• On a class of special linear systems of P³
• Biliaison classes of curves in P³
• Rational cuspidal plane curves of type (d, d-3)
• The action of the Cremona group on rational curves of ℙ³