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2022 Explicit computation of symmetric differentials and its application to quasihyperbolicity
Nils Bruin, Jordan Thomas, Anthony Várilly-Alvarado
Algebra Number Theory 16(6): 1377-1405 (2022). DOI: 10.2140/ant.2022.16.1377

Abstract

We develop explicit techniques to investigate algebraic quasihyperbolicity of singular surfaces through the constraints imposed by symmetric differentials. We apply these methods to prove that rational curves on Barth’s sextic surface, apart from some well-known ones, must pass through at least four singularities, and that genus 1 curves must pass through at least two. On the surface classifying perfect cuboids, our methods show that rational curves, again apart from some well-known ones, must pass through at least seven singularities, and that genus 1 curves must pass through at least two.

We also improve lower bounds on the dimension of the space of symmetric differentials on surfaces with A1-singularities, and use our work to show that Barth’s decic, Sarti’s surface, and the surface parametrizing 3×3 magic squares of squares are all algebraically quasihyperbolic.

Citation

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Nils Bruin. Jordan Thomas. Anthony Várilly-Alvarado. "Explicit computation of symmetric differentials and its application to quasihyperbolicity." Algebra Number Theory 16 (6) 1377 - 1405, 2022. https://doi.org/10.2140/ant.2022.16.1377

Information

Received: 14 April 2020; Revised: 9 April 2021; Accepted: 5 October 2021; Published: 2022
First available in Project Euclid: 2 October 2022

Digital Object Identifier: 10.2140/ant.2022.16.1377

Subjects:
Primary: 14J60 , 14Q10
Secondary: 14J25 , 14J29 , 14M10

Keywords: algebraic hyperbolicity , nodal surfaces , symmetric differentials

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.16 • No. 6 • 2022
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