%0 Journal Article
%T The cohomological support locus of pluricaonical sheaves and the Iitaka fibration
%A Lei Zhang
%J Mathematics
%D 2012
%I arXiv
%R 10.1016/j.ssc.2012.10.042
%X Let $alb_X: X \rightarrow A$ be the Albanese map of a smooth projective variety and $f: X \rightarrow Y$ the fibration from the Stein factorization of $alb_X$. For a positive integer $m$, if $f$ and $m$ satisfy the assumptions AS(1,2), then the translates through the origin of all components of cohomological locus $V^0(\omega_X^m, alb_X)$ generates $I^*Pic^0(S)$ where $I: X \rightarrow S$ denotes the Iitaka fibration. This result applies to studying pluricanonical maps. We also considered the problem about whether a fibration is isotrivial and isogenous to a product.
%U http://arxiv.org/abs/1212.3757v2