Moduli space of stable curves from a homotopy viewpoint
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.
Satake compactification of the Siegel modular varieties
scientific article; zbMATH DE number 3847555