Number Theory--On the existence of covers of [P.sub.1] associated to certain permutations, by PIETRO CORVAJA and UMBERTO ZANNIER, communicated on November 10, 2017

Number Theory--On the existence of covers of [P.sub.1] associated to certain permutations, by PIETRO CORVAJA and UMBERTO ZANNIER, communicated on November 10, 2017

In this short note we prove the impossibility of realizing finite topological covers of the Riemann sphere minus three points, associated to certain explicit combinatorial (permutation) data. This comes from a question of M. Zieve and falls in the framework of the so-called "Hurwitz problem&quo...

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Veröffentlicht in:Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni 2018-06, Vol.29 (2), p.289
Hauptverfasser: Corvaja, Pietro, Zannier, Umberto
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Mathematical research
Permutations
Riemann surfaces
Set theory
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description In this short note we prove the impossibility of realizing finite topological covers of the Riemann sphere minus three points, associated to certain explicit combinatorial (permutation) data. This comes from a question of M. Zieve and falls in the framework of the so-called "Hurwitz problem", asking for a "simple" description of the combinatorial data which can be so realized. KEY WORDS: Permutations, covers (of curves), branching MATHEMATICS SUBJECT CLASSIFICATION: 14H57, 05E99
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subjects Mathematical research
Permutations
Riemann surfaces
Set theory
title Number Theory--On the existence of covers of [P.sub.1] associated to certain permutations, by PIETRO CORVAJA and UMBERTO ZANNIER, communicated on November 10, 2017
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