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September 2020 Moduli spaces for dynamical systems with portraits
John R. Doyle, Joseph H. Silverman
Illinois J. Math. 64(3): 375-465 (September 2020). DOI: 10.1215/00192082-8642523

Abstract

A portrait P on P N is a pair of finite point sets Y X P N , a map Y X , and an assignment of weights to the points in Y . We construct a parameter space End d N [ P ] whose points correspond to degree d endomorphisms f : P N P N such that f : Y X is as specified by a portrait P , and prove the existence of the GIT quotient moduli space M d N [ P ] : = End d N / / SL N + 1 under the SL N + 1 -action ( f , Y , X ) ϕ = ( ϕ 1 f ϕ , ϕ 1 ( Y ) , ϕ 1 ( X ) ) relative to an appropriately chosen line bundle. We also investigate the geometry of M d N [ P ] and give two arithmetic applications.

Citation

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John R. Doyle. Joseph H. Silverman. "Moduli spaces for dynamical systems with portraits." Illinois J. Math. 64 (3) 375 - 465, September 2020. https://doi.org/10.1215/00192082-8642523

Information

Received: 27 March 2019; Revised: 30 April 2020; Published: September 2020
First available in Project Euclid: 1 July 2020

zbMATH: 07235509
MathSciNet: MR4132597
Digital Object Identifier: 10.1215/00192082-8642523

Subjects:
Primary: 37P45
Secondary: 37P15

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 3 • September 2020
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