On the topology of real algebraic stacks
Algebraic Geometry
2025-10-27 v3 Algebraic Topology
General Topology
Abstract
Motivated by questions arising in the theory of moduli spaces in real algebraic geometry, we develop a range of methods to study the topology of the real locus of a Deligne-Mumford stack over the real numbers. As an application, we verify in several cases the Smith-Thom type inequality for stacks that we conjectured in an earlier work. This requires combining techniques from group theory, algebraic geometry, and topology.
Keywords
Cite
@article{arxiv.2504.02720,
title = {On the topology of real algebraic stacks},
author = {Emiliano Ambrosi and Olivier de Gaay Fortman},
journal= {arXiv preprint arXiv:2504.02720},
year = {2025}
}
Comments
v1: 41 pages, 6 figures, comments welcome. v2: added Corollary 3.8. v3: added Theorems 1.4 and 1.5