No abstract

Abstract. Let alb X : X → Alb(X) be the Albanese map of a smooth projective variety and f : X → Y the fibration arising from the Stein factorization of alb X . For a positive integer m, if f and m satisfy two certain assumptions AS(1, 2), then the translates through the origin of all components of cohomological locus V 0 (ω m X , alb X ) ⊂ Pic 0 (X) generates I * Pic 0 (S) where I : X → S denotes the Iitaka fibration. As an application, we study pluri-canonical maps.