Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 43 min ago
PreprintarXiv licencearXiv

Generic reconstruction of rational maps from multipliers of periods one and two

  • Geng-Rui Zhang
Open at sourcePDFDOICite

Abstract

For every integer d≥2 and every field of characteristic different from $2$, we prove that on the moduli space ℳd of degree-d rational maps, the multiplier spectrum morphism formed from the periodic points of periods one and two is birational to the closure of its image. Consequently, over every algebraically closed field of characteristic different from $2$, it is generically injective, which proves a recent conjecture of Ji and Xie in characteristic zero. The proof uses a fixed-index normal form, a non-archimedean degeneration of two-cycles, and birational reconstruction of an affine fixed-point configuration from pair invariants.

Related

  1. Independence of multipliers via degenerations of rational maps
    Igors Gorbovickis
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv
  2. Zeros of E2, quasi-periods, and Schwarz maps
    Abdellah Sebbar
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Generic Linear Momentum Escape for Twist Maps
    Jianxing Du
    arXivPreprintCC0Full textDynamical systemsarXiv
  4. Higher arithmetic degrees of dominant rational self-maps
    Nguyen-Bac Dang, Dragos Ghioca, Fei Hu +2
    Annali della Scuola Normale Superiore di Pisa. Classe di ScienzePeer-reviewedHAL deposit licenceFull text4 citedAlgebra & number theoryHAL
  5. Sharp degree bound for rational proper maps from 𝔹2 to 𝔹4
    Tianzhi Hu, Mai Shi, Pingsan Yuan
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{zhang2026generic,
  title = {{Generic reconstruction of rational maps from multipliers of periods one and two}},
  author = {Geng-Rui Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07383},
  eprint = {2609.07383},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07383},
}
RIS
TY  - UNPB
TI  - Generic reconstruction of rational maps from multipliers of periods one and two
AU  - Geng-Rui Zhang
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07383
UR  - https://arxiv.org/abs/2609.07383
AB  - For every integer d≥2 and every field of characteristic different from $2$, we prove that on the moduli space ℳ_d of degree-d rational maps, the multiplier spectrum morphism formed from the periodic points of periods one and two is birational to the closure of its image. Consequently, over every algebraically closed field of characteristic different from $2$, it is generically injective, which proves a recent conjecture of Ji and Xie in characteristic zero. The proof uses a fixed-index normal form, a non-archimedean degeneration of two-cycles, and birational reconstruction of an affine fixed-point configuration from pair invariants.
ER  -