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Towards Categorical Kähler Geometry

  • Fabian Haiden
  • Ludmil Katzarkov
  • Maxim Kontsevich
  • Pranav Pandit
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Abstract

We outline the contours of an emerging theory of Kähler metrics in derived noncommutative geometry. This is a refinement of the theory of Bridgeland stability conditions encoding underlying differential-geometric structures. We propose elements of such a structure in both Archimedean and non-Archimedean settings, including metrized objects, mass measures satisfying a BPS inequality, harmonic metrics, minimizing flows, and complexified Kähler potentials. We develop the framework through examples and constructions involving Fukaya categories, quiver representations and associated C*-algebras, spectral networks, and comonadic adjunctions of stable ∞-categories.

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Cite

BibTeXRIS
BibTeX
@misc{haiden2026towards,
  title = {{Towards Categorical Kähler Geometry}},
  author = {Fabian Haiden and Ludmil Katzarkov and Maxim Kontsevich and Pranav Pandit},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00978},
  eprint = {2609.00978},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00978},
}
RIS
TY  - UNPB
TI  - Towards Categorical Kähler Geometry
AU  - Fabian Haiden
AU  - Ludmil Katzarkov
AU  - Maxim Kontsevich
AU  - Pranav Pandit
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00978
UR  - https://arxiv.org/abs/2609.00978
AB  - We outline the contours of an emerging theory of Kähler metrics in derived noncommutative geometry. This is a refinement of the theory of Bridgeland stability conditions encoding underlying differential-geometric structures. We propose elements of such a structure in both Archimedean and non-Archimedean settings, including metrized objects, mass measures satisfying a BPS inequality, harmonic metrics, minimizing flows, and complexified Kähler potentials. We develop the framework through examples and constructions involving Fukaya categories, quiver representations and associated C^*-algebras, spectral networks, and comonadic adjunctions of stable ∞-categories.
ER  -