HMS symmetries and hypergeometric systems. (English) Zbl 1523.14036

Špenko, Špela

Hujdurović, Ademir (ed.) et al., European congress of mathematics. Proceedings of the 8th congress, 8ECM, Portorož, Slovenia, June 20–26, 2021. Berlin: European Mathematical Society (EMS). 489-510 (2023).

Summary: The derived category of an algebraic variety might be a source of a myriad of new (categorical) symmetries. Some are predicted by homological mirror symmetry, to be obtained from the fundamental group of the space of complex structures of its mirror partner. These finally lead to differential equations. We expositorily unravel a part of this conjectural master plan for a class of toric varieties.
For the entire collection see [Zbl 1519.00033].

MSC:

14F08	Derived categories of sheaves, dg categories, and related constructions in algebraic geometry
14J33	Mirror symmetry (algebro-geometric aspects)
13A50	Actions of groups on commutative rings; invariant theory
53D37	Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category
32S45	Modifications; resolution of singularities (complex-analytic aspects)
16S38	Rings arising from noncommutative algebraic geometry
14F06	Sheaves in algebraic geometry

Keywords:

Riemann-Hilbert correspondence; homological mirror symmetry; geometric invariant theory

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