Evidence to subcanonicity of codimension two subvarieties of G(1,4)

Abstract

In this paper, we show that any smooth subvariety of codimension two in G(1,4) (the Grassmannian of lines of P-4) of degree at most 25 is subcanonical. Analogously, we prove that smooth subvarieties of codimension two in G(1,4) that are not of general type have degree <= 32 and we classify all of them. In both classifications, any subvariety in the final list is either a complete intersection or the zero locus of a section of a twist of the rank-two universal bundle on G(1,4).