Quadratic differentials as stability conditions: Collapsing subsurfaces-Reference-Cited by-同舟云学术

Quadratic differentials as stability conditions: Collapsing subsurfaces

Published:2024-02-21 Issue:0 Volume:0 Page:
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Barbieri Anna¹^ORCID,Möller Martin²,Qiu Yu³,So Jeonghoon²

Affiliation:

1. Dipartimento di Informatica – Settore Matematica , 19051 Università di Verona , Strada Le Grazie 15, 37134 Verona , Italy

2. Institut für Mathematik , Goethe-Universität Frankfurt , Robert-Mayer-Str. 6–8, 60325 Frankfurt am Main , Germany

3. Yau Mathematical Sciences Center and Department of Mathematical Sciences , 12442 Tsinghua University , 100084; and Beijing Institute of Mathematical Sciences and Applications, Yanqi Lake , Beijing , P. R. China

Abstract

Abstract We introduce a new class of triangulated categories, which are Verdier quotients of three-Calabi–Yau categories from (decorated) marked surfaces, and show that its spaces of stability conditions can be identified with moduli spaces of framed quadratic differentials on Riemann surfaces with arbitrary order zeros and arbitrary higher order poles. A main tool in our proof is a comparison of two exchange graphs, obtained by tilting hearts in the quotient categories and by flipping mixed angulations associated with the quadratic differentials.

Funder

European Research Council

Deutsche Forschungsgemeinschaft

National Key Research and Development Program of China

Natural Science Foundation of Beijing Municipality

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2024-0005/pdf

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