1993/01/20 by A. Aure, Alf Bjørn Aure, W. Decker +12
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9301004
28 pages. AMSLaTeX 1.1
arxiv created 1993/01/20 · arxiv updated 2009/11/30
In 1988 Serrano \citeSer, using Reider's method, discovered a minimal bielliptic surface in \PP4. Actually he showed that there is a unique family of such surfaces and that they have degree 10 and sectional genus 6. In this paper we describe, among other things, the geometry of the embedding of the minimal bielliptic surfaces. A consequence of this description will be the existence of smooth nonminimal bielliptic surfaces of degree 15 in \PP4. We also explain how to construct the degree 15 surfaces with the help of the quadro-cubic Cremona transformation of \PP4. Finally, we remark that the quintic elliptic scroll and the abelian and bielliptic surfaces of degree 10 and 15 are essentially the only smooth irregular surfaces known in \PP4 (all others can be derived via finite morphisms \PP4→\PP4 ).