Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Syzygies of compact complex hyperbolic manifolds


Authors: Jun-Muk Hwang and Wing-Keung To
Journal: J. Algebraic Geom. 22 (2013), 175-200
DOI: https://doi.org/10.1090/S1056-3911-2012-00578-5
Published electronically: April 17, 2012
MathSciNet review: 2993051
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Abstract | References | Additional Information

Abstract: We give a sufficient condition for the pluri-canonical bundles of a compact complex hyperbolic manifold to satisfy the property $ (N_p)$ on linear syzygies in terms of the hyperbolic injectivity radius. In the process, we obtain sharp lower bounds for the volumes of one-dimensional complex analytic subvarieties in geodesic tubular neighborhoods of the Cartesian self-product of a compact complex hyperbolic manifold.


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Additional Information

Jun-Muk Hwang
Affiliation: Korea Institute for Advanced Study, Hoegiro 87, Seoul, 130-722, Korea
Email: jmhwang@kias.re.kr

Wing-Keung To
Affiliation: Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076
Email: mattowk@nus.edu.sg

DOI: https://doi.org/10.1090/S1056-3911-2012-00578-5
Received by editor(s): April 28, 2010
Received by editor(s) in revised form: November 23, 2010
Published electronically: April 17, 2012
Additional Notes: The first author was supported by National Researcher Program 2010-0020413 of NRF and MEST. The second author was partially supported by the research grant R-146-000-106-112 from the National University of Singapore and the Ministry of Education.

American Mathematical Society