On the singular nerve of the moduli space of compact Riemann surfaces
Volume 245 / 2019
Fundamenta Mathematicae 245 (2019), 127-148
MSC: Primary 30F35, 14H10; Secondary 32G15, 20F05, 14H20.
DOI: 10.4064/fm469-7-2018
Published online: 10 January 2019
Abstract
The singular locus of the moduli space of compact Riemann surfaces of a given genus is known to be the union of certain canonical subsets which can be more easily understood than the whole singular locus itself. However, in order to obtain a global picture (not only a local one) via a description of the glueing, and so to understand the singular locus, the essential issue is to understand the intersection behaviour of these subsets. We study it by means of the nerve of this decomposition, which is a simplicial complex whose geometrical and homological dimensions we investigate.
