Geography of the Teichmüller stack
arXiv:2409.00072
Abstract
In this article, we describe the geography of the Teichmüller stack of \cite{LMStacks} and of one of its variants we introduce here, giving some answers to questions as: which points are orbifold points? What are the different local models of special points?... We give a rough description in the general case, and we use the compacity of the cycle spaces to get a much more detailed picture in the Kähler setting.
This paper subsumes arXiv:1709.07237 v2 : section 12 completely rewritten and main conjecture expanded