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Transactions of the American Mathematical Society

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Cohomological support loci of varieties of Albanese fiber dimension one

Authors: Zhi Jiang and Hao Sun
Journal: Trans. Amer. Math. Soc. 367 (2015), 103-119
MSC (2010): Primary 14E05
Published electronically: June 16, 2014
MathSciNet review: 3271255
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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 $ \vert 4K_X\vert$ induces a birational map of $ X$.

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Additional Information

Zhi Jiang
Affiliation: Mathématiques Bâtiment 425, Université Paris-Sud, F-91405 Orsay, France

Hao Sun
Affiliation: Department of Mathematics, Huazhong Normal University, Wuhan 430079, People’s Republic of China
Address at time of publication: Department of Mathematics, Shanghai Normal University, Shanghai 200234, People’s Republic of China

Keywords: Irregular variety, pluricanonical map, $M$-regularity
Received by editor(s): April 13, 2012
Received by editor(s) in revised form: September 21, 2012
Published electronically: June 16, 2014
Additional Notes: The second author was partially supported by the Mathematical Tianyuan Foundation of China (No. 11126192).
Article copyright: © Copyright 2014 American Mathematical Society

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