On algebraic fiber spaces over varieties of maximal Albanese dimension

الأصل · EN

We study algebraic fiber spaces f:X Y where Y is of maximal Albanese dimension. In particular we give an effective version a theorem of Kawamata: If Pₘ(X)=1 for some m ≥ 2, then the Albanese map of X is surjective. Combining this with CH it follows that X is birational to an abelian variety if and only if P₂(X)=1 and q(X)= dim (X).