On varieties of maximal Albanese dimension

Details On varieties of maximal Albanese dimension On varieties of maximal Albanese dimension

2009-09-25

arxiv.org/abs/0909.4817v2

Mathematics

Algebraic Geometry

We add a section about pluricanonical map; updated references;comments welcome

Scientific paper

Let $f: X\to Y$ be a surjective morphism of smooth $n$-dimensional projective varieties, with $Y$ of maximal Albanese dimension. Hacon and Pardini studied the structure of $f$ assuming $P_m(X)=P_m(Y)$ for some $m\geq 2$. We extend their result by showing that, under the above assumtions, $f$ is birationally equivalent to a quotient by a finite abelian group. We also study the pluricanonical map of varieties of maximal Albanese dimesnion. The main result is that the linear series $|5K_X|$ incuces the Iitaka model of $X$.

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