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Effective non-vanishing of asymptotic adjoint syzygies


Author: Xin Zhou
Journal: Proc. Amer. Math. Soc. 142 (2014), 2255-2264
MSC (2010): Primary 13D02; Secondary 14C99
DOI: https://doi.org/10.1090/S0002-9939-2014-11947-2
Published electronically: April 4, 2014
MathSciNet review: 3195751
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Abstract: The purpose of this paper is to establish an effective non-vanishing theorem for the syzygies of an adjoint-type line bundle on a smooth variety as the positivity of the embedding increases. Our purpose here is to show that for an adjoint-type divisor $ B = K_X+ bA$ with $ b \geq n+1$, one can obtain an effective statement for arbitrary $ X$ which specializes to the statement for Veronese syzygies in the paper ``Asymptotic Syzygies of Algebraic Varieties'' by Ein and Lazarsfeld. We also give an answer to Problem 7.9 in that paper in this setting.


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Additional Information

Xin Zhou
Affiliation: Department of Mathematics, University of Michigan, East Hall, 530 Church Street, Ann Arbor, Michigan 48109-1043
Email: paulxz@umich.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11947-2
Received by editor(s): March 31, 2012
Received by editor(s) in revised form: July 16, 2012
Published electronically: April 4, 2014
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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