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:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1237928
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact