Singular locus of rational ruled surfaces

2001/01/10 by Nicolas Perrin, Perrin, Nicolas
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #math.AG #msc:14F05 #msc:14J26 #msc:14N05

paper · pdf · doi:10.48550/arxiv.math/0101083

In french, 25 pages. Many improvements in the proofs. New results included : the study of GIT properties of the morphism and the study of the singular locus of the image. We prove that the image is rational

arxiv created 2001/10/04 · arxiv updated 2009/11/30

Abstract

We prove that the morphism that maps a rational ruled surface to its singular locus is genericaly injective modulo isomophism and duality. We also calculate the dimension and the degre of its image.

Related

• Ruled and rational surfaces and their models
• Rational maps from products of curves to surfaces with p_g = q = 0
• Rational maps and K3 surfaces
• Rational surfaces on low degree hypersurfaces
• On rational maps from a general surface in P³ to surfaces of general type