Perverse schobers, stability conditions and quadratic differentials

Fuente: arXiv
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Main Authors: Christ, Merlin, Haiden, Fabian, Qiu, Yu
Format: Preprint
Published: 2023
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author Christ, Merlin
Haiden, Fabian
Qiu, Yu
author_facet Christ, Merlin
Haiden, Fabian
Qiu, Yu
contents 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).
format Preprint
id arxiv_https___arxiv_org_abs_2303_18249
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Perverse schobers, stability conditions and quadratic differentials
Christ, Merlin
Haiden, Fabian
Qiu, Yu
Representation Theory
Algebraic Geometry
Geometric Topology
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).
title Perverse schobers, stability conditions and quadratic differentials
topic Representation Theory
Algebraic Geometry
Geometric Topology
url https://arxiv.org/abs/2303.18249