Irregular elliptic surfaces of degree 12 in projective fourspace

So far a few families of smooth irregular surfaces are known to exist in ?⁴ up to pullbacks by suitable finite morphisms from ?⁴ onto ?⁴ itself. In this paper we present two different constructions of irregular smooth minimal elliptic surfaces of degree 12 in ?⁴. 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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)