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arXiv · 2609.00978

Towards Categorical K\"ahler Geometry

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

We outline the contours of an emerging theory of K\"ahler 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 K\"ahler 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 $\infty$-categories.

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Fabian Haiden, Ludmil Katzarkov, Maxim Kontsevich, Pranav Pandit. 2026-09-01. Towards Categorical K\"ahler Geometry. https://arxiv.org/abs/2609.00978

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