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
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
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