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Quantitative geometric and arithmetic results on projective surfaces


Author: Hungzen Liao
Journal: Proc. Amer. Math. Soc. 145 (2017), 2495-2504
MSC (2010): Primary 32H30, 32H22, 11J97
DOI: https://doi.org/10.1090/proc/13401
Published electronically: November 29, 2016
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Abstract: In this paper, we improve Ru's defect relation and the height inequality in the case when $ X$ is a normal projective surface and $ D_j$, $ 1 \leq j \leq q$, are big and asymptotic free divisors without irreducible common components on $ X$. As a consequence, we derive a sharp result in the qualitative statement.


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Additional Information

Hungzen Liao
Affiliation: Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, Texas 77004
Email: lhungzen@math.uh.edu

DOI: https://doi.org/10.1090/proc/13401
Received by editor(s): November 30, 2015
Received by editor(s) in revised form: March 25, 2016, June 8, 2016, and July 12, 2016
Published electronically: November 29, 2016
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2016 American Mathematical Society