June 2023 On surjective homomorphisms from a configuration space group to a surface group
Koichiro SAWADA
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Hokkaido Math. J. 52(2): 253-266 (June 2023). DOI: 10.14492/hokmj/2021-526

Abstract

In the present paper, we classify all surjective homomorphisms from the étale fundamental group of the configuration space of a hyperbolic curve (over an algebraically closed field of characteristic zero) to the étale fundamental group of a hyperbolic curve. We can show that such a surjective homomorphism is necessarily “geometric” in some sense, that is, it factors through one of the homomorphisms which arise from specific morphisms of schemes.

Acknowledgment

I would like to thank Professor Akio Tamagawa for valuable discussions and advice. I would also like to thank the referee for the careful reading and insightful comments. This research was supported by JSPS KAKENHI Grant Numbers JP17J11423, JP20J00323.

Citation

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Koichiro SAWADA. "On surjective homomorphisms from a configuration space group to a surface group." Hokkaido Math. J. 52 (2) 253 - 266, June 2023. https://doi.org/10.14492/hokmj/2021-526

Information

Received: 13 April 2021; Revised: 15 March 2022; Published: June 2023
First available in Project Euclid: 9 July 2023

Digital Object Identifier: 10.14492/hokmj/2021-526

Subjects:
Primary: 14H30 , 20F36

Keywords: configuration space , fundamental group , hyperbolic curve , surjective homomorphism

Rights: Copyright c 2023 Hokkaido University, Department of Mathematics

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Vol.52 • No. 2 • June 2023
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