On varieties of maximal Albanese dimension

Abstract

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 $m\ge 2$. 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 $X$.

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

References in corpus (2)

• The Severi inequality $K^2\ge 4\chi$ for surfaces of maximal Albanese dimension
• Regularity on abelian varieties III: relationship with Generic Vanishing and applications

Cited by in corpus (2)

• On the Iitaka fibration of varieties of maximal Albanese dimension
• Syzygies, Pluricanonical Maps, and the Birational Geometry of Varieties of Maximal Albanese Dimension