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
- Email: firstname.lastname@example.org
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- 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
- MathSciNet review: 3195751