A compactification of the moduli space of self-maps of ℂℙ¹ via stable maps

Schmitt, Johannes

doi:10.1090/ecgd/313

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

Conform. Geom. Dyn. 21 (2017), 273-318

DOI: https://doi.org/10.1090/ecgd/313

Published electronically: October 12, 2017

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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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