Cohomological support loci of varieties of Albanese fiber dimension one

Jiang, Zhi; Sun, Hao

doi:10.1090/S0002-9947-2014-05997-7

Cohomological support loci of varieties of Albanese fiber dimension one
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Trans. Amer. Math. Soc. 367 (2015), 103-119 Request permission

Abstract:

Let $X$ be a smooth projective variety of Albanese fiber dimension 1 and of general type. We prove that the translates through $0$ of all components of $V^0(\omega _X)$ generate $\operatorname {Pic}^0(X)$. We then study the pluricanonical maps of $X$. We show that $|4K_X|$ induces a birational map of $X$.

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