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Proceedings of the American Mathematical Society

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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
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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Xin Zhou
Affiliation: Department of Mathematics, University of Michigan, East Hall, 530 Church Street, Ann Arbor, Michigan 48109-1043

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.