Abstract
In this paper, we describe the semistable quotient of the set of regular polynomial automorphisms \({\mathcal {H}}_2^2\) in the semistable locus of the moduli space of quadratic rational maps, using the portrait moduli space of rational maps with a fixed point. We also provide the parametrization of \({\mathcal {H}}_2^2\) using two invariants, \(\det f\) and \({\text {tr}}\,f\).
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Acknowledgements
The authors would like to thank Joseph H. Silverman for useful discussions and comments, thank the reviewer for helpful suggestions, and thank Brown University for its hospitality.
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This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education. (NRF-2016R1D1A1B01009208).
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Kwon, H., Lee, C.G. & Lee, SM. Regular polynomial automorphisms in the space of planar quadratic rational maps. J. Fixed Point Theory Appl. 22, 84 (2020). https://doi.org/10.1007/s11784-020-00819-z
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DOI: https://doi.org/10.1007/s11784-020-00819-z