On algebraic fiber spaces over varieties of maximal Albanese dimension

2000/11/07 by Jungkai A. Chen, Chen, Jungkai A., Christopher D. Hacon +1
Mathematics · #14F17 #14J10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F17 #msc:14J10

paper · pdf · doi:10.48550/arxiv.math/0011042

arxiv created 2000/11/07 · arxiv updated 2009/11/30

Abstract

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

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