Perverse schobers, stability conditions and quadratic differentials
Abstract
We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differentials. This approach is based on the notion of a perverse schober (perverse sheaf of triangulated categories) and their triangulated categories of global sections. Under suitable conditions on the perverse schober, we identify mixed-angulations and their flips with finite-length hearts and their tilts, which then leads to the identification of moduli spaces. As an application we obtain a generalization of the results of Bridgeland--Smith to quadratic differentials with arbitrary singularity type (zero/pole/exponential).
Cite
@article{arxiv.2303.18249,
title = {Perverse schobers, stability conditions and quadratic differentials},
author = {Merlin Christ and Fabian Haiden and Yu Qiu},
journal= {arXiv preprint arXiv:2303.18249},
year = {2024}
}
Comments
v5: The paper has been split into two parts, with the first focusing on tilting, arc system kits, and stability conditions, and the second focusing on relative graded Brauer graph algebras