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Chow Quotient Moduli Space of Dynamical Systems on the Projective Line and Rescaling Limits

  • Rin Gotou
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Abstract

We study Chow-quotient compactifications of the moduli space of degree-d rational self-maps of the projective line. We compute the degree of every three-dimensional orbit cycle in the Clebsch--Gordan compactification in terms of the main component and the hole depths. As consequences, we obtain the generic orbit class and a rational map on Chow quotients induced by iteration. We also introduce a marked Chow quotient designed to record collections of rescaling limits, describe it by decorated trees, and extend the fixed-point multiplier map to the normalization of the unmarked Chow quotient.

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Cite

BibTeXRIS
BibTeX
@misc{gotou2026chow,
  title = {{Chow Quotient Moduli Space of Dynamical Systems on the Projective Line and Rescaling Limits}},
  author = {Rin Gotou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07668},
  eprint = {2609.07668},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07668},
}
RIS
TY  - UNPB
TI  - Chow Quotient Moduli Space of Dynamical Systems on the Projective Line and Rescaling Limits
AU  - Rin Gotou
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07668
UR  - https://arxiv.org/abs/2609.07668
AB  - We study Chow-quotient compactifications of the moduli space of degree-d rational self-maps of the projective line. We compute the degree of every three-dimensional orbit cycle in the Clebsch--Gordan compactification in terms of the main component and the hole depths. As consequences, we obtain the generic orbit class and a rational map on Chow quotients induced by iteration. We also introduce a marked Chow quotient designed to record collections of rescaling limits, describe it by decorated trees, and extend the fixed-point multiplier map to the normalization of the unmarked Chow quotient.
ER  -