2023/10/21 by Lanteri, Antonio, Novelli, Carla
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.13987
Let Y be a smooth projective variety of dimension n ≥ 2 endowed with a finite morphism ϕ:Y → \mathbb Pn of degree 3, and suppose that Y, polarized by some ample line bundle, is a scroll over a smooth variety X of dimension m. Then n ≤ 3 and either m=1 or 2. When m=1, a complete description of the few varieties Y satisfying these conditions is provided. When m=2, various restrictions are discussed showing that in several instances the possibilities for such a Y reduce to the single case of the Segre product \mathbb P2 × \mathbb P1. This happens, in particular, if Y is a Fano threefold as well as if the base surface X is \mathbb P2.