Calabi-Yau Deformation Quantization

Jakob Ulmer

Calabi-Yau Deformation Quantization

Quantum Algebra 2026-07-28 v1 High Energy Physics - Theory Algebraic Geometry Algebraic Topology

Authors: Jakob Ulmer

Abstract

We record the Calabi-Yau version of Kontsevich's formality morphism from deformation quantization. As a special case we find that any unimodular holomorphic Poisson Calabi-Yau has a canonical closed deformation quantization of its resolved algebra of functions. A broader motivation is to find an explanation of Kontsevich's deformation quantization in the setting of Calabi-Yau categories via Sen-Zwiebach's string vertices.

Cite

@article{arxiv.2607.25438,
  title  = {Calabi-Yau Deformation Quantization},
  author = {Jakob Ulmer},
  journal= {arXiv preprint arXiv:2607.25438},
  year   = {2026}
}

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12 pages