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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Algebraic hyperbolicity for surfaces in toric threefolds

Authors: Christian Haase and Nathan Ilten
Journal: J. Algebraic Geom. 30 (2021), 573-602
Published electronically: January 14, 2021
MathSciNet review: 4283552
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Abstract | References | Additional Information

Abstract: Adapting focal loci techniques used by Chiantini and Lopez, we provide lower bounds on the genera of curves contained in very general surfaces in Gorenstein toric threefolds. We illustrate the utility of these bounds by obtaining results on algebraic hyperbolicity of very general surfaces in toric threefolds.

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Additional Information

Christian Haase
Affiliation: Institut für Mathematik, Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany
MR Author ID: 661101
ORCID: 0000-0003-4078-0913

Nathan Ilten
Affiliation: Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada
MR Author ID: 864815

Received by editor(s): May 9, 2019
Received by editor(s) in revised form: March 5, 2020
Published electronically: January 14, 2021
Additional Notes: The work of the first author was partially supported by the grant HA 4383/8-1 of the German Research Foundation DFG. The work of the second author was partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund
Article copyright: © Copyright 2021 University Press, Inc.