Non-general type surfaces in P4, an update

2026/07/18 by Hirotachi Abo, Kristian Ranestad, Frank-Olaf Schreyer
#math.AG

paper · pdf

Abstract

A general algebraic surface cannot be embedded in P4. Proving a conjecture by Hartshorne and Lichtenbaum, Ellingsrud and Peskine showed that there is a degree bound for smooth rational surfaces in P4, and in fact for surfaces not of general type. We give a survey of the classification status and of classical and computer-aided constructions of smooth non-general type surfaces in P4.

Related

• A smooth surface in P4 not of general type has degree at most 66
• Examples of smooth non-general type surfaces in P⁴
• A smooth surface in P4 not of general type has degree at most 46
• An improved bound for the degree of smooth surfaces in P4 not of general type.
• Boundedness for surfaces in weighted P⁴