EVIDENCE TO SUBCANONICITY OF CODIMENSION TWO SUBVARIETIES OF 𝔾(1,4)

In this paper, we show that any smooth subvariety of codimension two in 𝔾(1,4) (the Grassmannian of lines of ℙ4) 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).