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Examples of homological mirror symmetry via Zariski descent

  • James Pascaleff
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Abstract

This paper considers a general setting in which the Fukaya category of an exact symplectic manifold may be decomposed as a fiber product of Fukaya categories of smaller pieces. We establish a property of Fukaya categories that is mirror to Zariski descent of coherent sheaves. This fits into a natural strategy to prove homological mirror symmetry by a local-to-global analysis. The examples we consider in detail are open Riemann surfaces and exact log Calabi-Yau surfaces, and we provide proofs of homological mirror symmetry in these cases.

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Cite

BibTeXRIS
BibTeX
@misc{pascaleff2026examples,
  title = {{Examples of homological mirror symmetry via Zariski descent}},
  author = {James Pascaleff},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.14310},
  eprint = {2611.14310},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.14310},
}
RIS
TY  - UNPB
TI  - Examples of homological mirror symmetry via Zariski descent
AU  - James Pascaleff
PY  - 2026
DA  - 2026/11/10
PB  - arXiv
DO  - 10.48550/arxiv.2611.14310
UR  - https://arxiv.org/abs/2611.14310
AB  - This paper considers a general setting in which the Fukaya category of an exact symplectic manifold may be decomposed as a fiber product of Fukaya categories of smaller pieces. We establish a property of Fukaya categories that is mirror to Zariski descent of coherent sheaves. This fits into a natural strategy to prove homological mirror symmetry by a local-to-global analysis. The examples we consider in detail are open Riemann surfaces and exact log Calabi-Yau surfaces, and we provide proofs of homological mirror symmetry in these cases.
ER  -