Moduli space of stable curves from a homotopy viewpoint
type: Item
instance of: scholarly article
title: Moduli space of stable curves from a homotopy viewpoint
zbMATH Open document ID: 0534.14014
author: R. Lee
author: Ruth Charney
published in: Journal of Differential Geometry
publication date: 1984-01-01T00:00:00Z
review text: In a very broad sense, the authors establish a framework to study the algebraic topology of moduli spaces, arising from the deformation of projective varieties. More concretely, their main concern in the paper is the moduli space of stable curves, where the stable points form the classifying space of the mapping class group and the semistable points give a stratification of similar classifying spaces. Using the language of an abstract categorical construction, they describe the homotopy type of this moduli space of stable curves. The techniques and tools involved in this construction were originated from G. Segal and D. Quillen, and are well-known among algebraic topologists. As an application, they show how this abstract description can be used to study the classical period mapping between the moduli space of stable curves and the Satake compactification of the Siegel modular varieties. Their work, together with the work of E. Miller, gives a complete description of the induced mapping between the rational homology of these spaces.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 32G15
Mathematics Subject Classification ID: 55P15
Mathematics Subject Classification ID: 32G20
Mathematics Subject Classification ID: 32J05
zbMATH DE Number: 3847555
zbMATH Keywords: homotopy type of moduli space
zbMATH Keywords: moduli space of stable curves
zbMATH Keywords: period mapping
zbMATH Keywords: Satake compactification of the Siegel modular varieties
Wikidata QID: Q115187569
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214438997
OpenAlex ID: W1577713970
DOI: 10.4310/JDG/1214438997
description: scientific article; zbMATH DE number 3847555