Moduli for stable marked trees of projective lines
type: Item
instance of: scholarly article
title: Moduli for stable marked trees of projective lines
zbMATH Open document ID: 0723.14020
DOI: 10.1007/BF01445232
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164891
review text: The moduli theory for stable n-pointed trees of projective lines as developed by \textit{L. Gerritzen}, the author and \textit{M. van der Put} [Indagationes Math. 50, No.2, 131-163 (1988; Zbl 0698.14019)] is extended to the case of an infinite set M of markings. This is the setting which is relevant for the uniformization theory of stable Riemann surfaces [cf. \textit{L. Gerritzen} and the author, J. Reine Angew. Math. 389, 190-208 (1988; Zbl 0639.30040)]. Although the final results are formally analogous to the case of a finite set of markings, new technical tools had to be developed even to state the results: since neither the classified objects nor (in general) the moduli spaces are varieties (or schemes), one has to work in the category of provarieties (or projective limits of varieties). We also need new definitions of trees (not relying on edges or on topological properties), of trees of projective lines, and of intersection graphs. The main result states the existence of fine moduli spaces for stable M- marked trees of projective lines, and for trees where the M marking is equivariant with respect to a given group action.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14D22
Mathematics Subject Classification ID: 14A20
zbMATH DE Number: 4191867
zbMATH Keywords: n-pointed trees of projective lines
zbMATH Keywords: uniformization theory of stable Riemann surfaces
zbMATH Keywords: markings
zbMATH Keywords: provarieties
zbMATH Keywords: fine moduli spaces
author: Frank Herrlich
reviewed by: Frank Herrlich
MaRDI profile type: Publication
cites work: Q3781347
cites work: Q3475378
cites work: The extended Teichmüller space
cites work: The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$
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description: scientific article; zbMATH DE number 4191867