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Algebraic hyperbolicity of very general surfaces

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Abstract

Recently, Haase and Ilten initiated the study of classifying algebraically hyperbolic surfaces in toric threefolds. We complete this classification for \({\mathbb{P}^1} \times {\mathbb{P}^1} \times {\mathbb{P}^1},\,\,{\mathbb{P}^2} \times {\mathbb{P}^1},\,\,{\mathbb{F}_e} \times {\mathbb{P}^1}\) and the blowup of ℙ3 at a point, augmenting our earlier work on ℙ3. Most importantly, we treat the boundary cases which are the hardest cases from the point of view of positivity. In the process, we codify several different techniques for proving algebraic hyperbolicity, allowing us to prove similar results for hypersurfaces in any threefold admitting a group action with dense orbit.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and CS, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Izzet Coskun

  2. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    Eric Riedl

Authors
  1. Izzet Coskun
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  2. Eric Riedl
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Correspondence to Izzet Coskun.

Additional information

During the preparation of this article the first author was partially supported by the NSF grant DMS-1500031 and NSF FRG grant DMS 1664296 and the second author was partially supported by the NSF RTG grant DMS-1246844 and AMS-Simons Travel grant.

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Coskun, I., Riedl, E. Algebraic hyperbolicity of very general surfaces. Isr. J. Math. 253, 787–811 (2023). https://doi.org/10.1007/s11856-022-2379-2

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  • DOI: https://doi.org/10.1007/s11856-022-2379-2

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