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The cohomological support locus of pluri-canonical sheaves and the Iitaka fibration
Abstract
Let albX : X → Alb(X) be the Albanese map of a smooth projective variety and f : X → Y the
fibration arising from the Stein factorization of albX. 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(ωm/X, albX) ⊂ Pic0(X) generate I∗Pic0(S), where I : X → S denotes the Iitaka fibration. As an application, we study pluri-canonical maps.
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