Irregular elliptic surfaces of degree 12 in the projective fourspace

2002/10/21 by Hirotachi Abo, Kristian Ranestad, Abo, Hirotachi +1
Mathematics · #14J27 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J27

paper · pdf · doi:10.48550/arxiv.math/0210317

16 pages

arxiv created 2002/10/21 · arxiv updated 2009/11/30

Abstract

So far only a few families of smooth irregular surfaces are known to exist in P⁴ up to pullbacks by suitable finite morphisms from P⁴ onto P⁴ itself. In this paper we present two different constructions of irregular smooth minimal elliptic surfaces of degree 12 in P⁴. The first is a monad construction while the other uses liaison. The family constructed via liaison includes the surfaces of the first family as a special case.

Related

• Examples of smooth non-general type surfaces in P⁴
• The Geometry of Bielliptic Surfaces in P⁴
• Syzygies of Abelian and Bielliptic Surfaces in P⁴
• Construction of rational surfaces of degree 12 in projective fourspace (with an appendix by Kristian Ranestad)
• An elliptic conic bundle in P⁴ arising from a stable rank-3 vector bundle