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Peer-reviewedCC BYCompositio Mathematica

Perverse schobers, stability conditions and quadratic differentials I

  • Merlin Christ1
  • Fabian Haiden2
  • Qiu Yu3
  1. 1Mathematisches Institut, Universität Bonn
  2. 2University of Southern Denmark
  3. 3Beijing Institute of Mathematical Sciences and Applications
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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 identification is based on the use of perverse schobers (perverse sheaves of triangulated categories) and a notion of positive arc system kit on a perverse schober script upper F F ℱ , which provides a systematic way of assigning to a graded curve on the surface a global section of script upper F F ℱ . This assignment allows us to identify mixed angulations and their flips with finite-length hearts and their tilts. As an application we obtain a generalization of the results of Bridgeland and Smith to quadratic differentials with arbitrary singularity type (zero/pole/exponential).

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Cite

BibTeXRIS
BibTeX
@article{christ2026perverse,
  title = {{Perverse schobers, stability conditions and quadratic differentials I}},
  author = {Merlin Christ and Fabian Haiden and Qiu Yu},
  journal = {Compositio Mathematica},
  year = {2026},
  month = sep,
  doi = {10.1017/s0010437x26103479},
  url = {https://doi.org/10.1017/s0010437x26103479},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Perverse schobers, stability conditions and quadratic differentials I
AU  - Merlin Christ
AU  - Fabian Haiden
AU  - Qiu Yu
PY  - 2026
DA  - 2026/09/01
JO  - Compositio Mathematica
DO  - 10.1017/s0010437x26103479
UR  - https://doi.org/10.1017/s0010437x26103479
AB  - 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 identification is based on the use of perverse schobers (perverse sheaves of triangulated categories) and a notion of positive arc system kit on a perverse schober script upper F F ℱ , which provides a systematic way of assigning to a graded curve on the surface a global section of script upper F F ℱ . This assignment allows us to identify mixed angulations and their flips with finite-length hearts and their tilts. As an application we obtain a generalization of the results of Bridgeland and Smith to quadratic differentials with arbitrary singularity type (zero/pole/exponential).
SN  - 0010-437X
SN  - 1570-5846
ER  -