A note on rational surfaces in projective four-space

1999/05/24 by Philippe Ellia, Ellia, Philippe
Mathematics · #14J26 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J26

paper · pdf · doi:10.48550/arxiv.math/9905148

PlainTex; to appear

arxiv created 1999/05/24 · arxiv updated 2009/11/30

Abstract

It is proved that a smooth rational surface in projective four-space, which is ruled by cubics or quartics has degree at most 12. It is also proved that a smooth rational surface in projective four-space which is the image of Fn by a linear system with "simple base points" (see text) has degree at most 12.

Related

• Construction of rational surfaces of degree 12 in projective fourspace (with an appendix by Kristian Ranestad)
• Exterior algebra methods for the construction of rational surfaces in the projective fourspace
• On smooth surfaces in projective four-space lying on quartic hypersurfaces with isolated singularities
• Rational surfaces in P⁴ containing a plane curve
• Counting rational points on smooth quartic and quintic surfaces