I will talk about the construction of a rational surface
of degree 12 in projective fourspace.
This surface is new and of interest in the classification of
smooth non-general type surfaces
in projective fourspace.
This classification problem is motivated by
the theorem of Ellingsrud and Peskine,
which says that the degrees of such surfaces are bounded.
Moreover, the rational surfaces in projective fourspace
were previously known up to degree 11.
This surface was found in collaboration with Frank-Olaf Schreyer.
Last Updated: March 10 2004 by Hirotachi Abo