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arXiv · 2610.38751

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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Patrik Hammer. 2026-10-28. Examples of rigid Twistor D-modules. https://arxiv.org/abs/2610.38751

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