Let π: X → B be a family whose general fibre Xb is a (d1, ⋯, da)-polarization on a general abelian variety, where 1 ≤ di ≤ 2, i = 1, ⋯, a and a ≥ 4. We show that the fibres are in the same birational class if all the (m, 0)-forms on Xb are liftable to (m, 0)-forms on X, where m = 1 and m = a - 1. Actually, we show a general criteria to establish whether the fibres of certain families belong to the same birational class.
On birationally trivial families and adjoint quadrics
Cesarano L.;Rizzi L.;Zucconi F.
2022-01-01
Abstract
Let π: X → B be a family whose general fibre Xb is a (d1, ⋯, da)-polarization on a general abelian variety, where 1 ≤ di ≤ 2, i = 1, ⋯, a and a ≥ 4. We show that the fibres are in the same birational class if all the (m, 0)-forms on Xb are liftable to (m, 0)-forms on X, where m = 1 and m = a - 1. Actually, we show a general criteria to establish whether the fibres of certain families belong to the same birational class.File in questo prodotto:
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