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Conformal Geometry and Dynamics

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A compactification of the moduli space of self-maps of $\mathbb {CP}^1$ via stable maps


Author: Johannes Schmitt
Journal: Conform. Geom. Dyn. 21 (2017), 273-318
MSC (2010): Primary 37F10, 14D23, 14L30
DOI: https://doi.org/10.1090/ecgd/313
Published electronically: October 12, 2017
MathSciNet review: 3711376
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Abstract: We present a new compactification $M(d,n)$ of the moduli space of self-maps of $\mathbb {CP}^1$ of degree $d$ with $n$ markings. It is constructed via GIT from the stable maps moduli space $\overline M_{0,n}(\mathbb {CP}^1 \times \mathbb {CP}^1, (1,d))$. We show that it is the coarse moduli space of a smooth Deligne-Mumford stack and we compute its rational Picard group.


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Additional Information

Johannes Schmitt
Affiliation: Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
MR Author ID: 1074251
Email: johannes.schmitt@math.ethz.ch

Received by editor(s): November 30, 2016
Received by editor(s) in revised form: July 25, 2017
Published electronically: October 12, 2017
Additional Notes: The author was supported by grant SNF-200020162928
Article copyright: © Copyright 2017 American Mathematical Society