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PreprintarXiv licencearXiv

Examples of rigid Twistor D-modules

  • Patrik Hammer
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Abstract

The well-established theory of D-modules gives a framework to study linear differential equations from the perspective of algebraic geometry. A significant advancement in this theory has been the introduction of Twistor D-modules by Claude Sabbah and Takuro Mochizuki: These objects expose inherent, but hidden information of the underlying differential equations in an elegant way. We explain the foundational concepts of Twistor D-modules and give concrete examples of these objects. We introduce a notion of rigidity for Twistor D-modules, which these examples fulfill. We conclude with a certain algebraicity conjecture about rigid Twistor D-modules, which we prove in a special case.

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Cite

BibTeXRIS
BibTeX
@misc{hammer2026examples,
  title = {{Examples of rigid Twistor D-modules}},
  author = {Patrik Hammer},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38751},
  eprint = {2610.38751},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38751},
}
RIS
TY  - UNPB
TI  - Examples of rigid Twistor D-modules
AU  - Patrik Hammer
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38751
UR  - https://arxiv.org/abs/2610.38751
AB  - The well-established theory of D-modules gives a framework to study linear differential equations from the perspective of algebraic geometry. A significant advancement in this theory has been the introduction of Twistor D-modules by Claude Sabbah and Takuro Mochizuki: These objects expose inherent, but hidden information of the underlying differential equations in an elegant way. We explain the foundational concepts of Twistor D-modules and give concrete examples of these objects. We introduce a notion of rigidity for Twistor D-modules, which these examples fulfill. We conclude with a certain algebraicity conjecture about rigid Twistor D-modules, which we prove in a special case.
ER  -