Algebraic stability of meromorphic maps descended from Thurston’s pullback maps
| Autor: | Rohini Ramadas |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Teichmüller space
Applied Mathematics General Mathematics 010102 general mathematics Periodic point Space (mathematics) 01 natural sciences Moduli space Combinatorics Cardinality Pullback 0103 physical sciences 010307 mathematical physics Branched covering 0101 mathematics Meromorphic function Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 374:565-587 |
| ISSN: | 1088-6850 0002-9947 |
| DOI: | 10.1090/tran/8221 |
| Popis: | Let ϕ : S 2 → S 2 \phi :S^2 \to S^2 be an orientation-preserving branched covering whose post-critical set has finite cardinality n n . If ϕ \phi has a fully ramified periodic point p ∞ p_{\infty } and satisfies certain additional conditions, then, by work of Koch, ϕ \phi induces a meromorphic self-map R ϕ R_{\phi } on the moduli space M 0 , n \mathcal {M}_{0,n} ; R ϕ R_{\phi } descends from Thurston’s pullback map on Teichmüller space. Here, we relate the dynamics of R ϕ R_{\phi } on M 0 , n \mathcal {M}_{0,n} to the dynamics of ϕ \phi on S 2 S^2 . Let ℓ \ell be the length of the periodic cycle in which the fully ramified point p ∞ p_{\infty } lies; we show that R ϕ R_{\phi } is algebraically stable on the heavy-light Hassett space corresponding to ℓ \ell heavy marked points and ( n − ℓ ) (n-\ell ) light points. |
| Databáze: | OpenAIRE |
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