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arXiv · 1902.03551

Doubly periodic monopoles and $q$-difference modules

Takuro Mochizuki
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Abstract

An interesting theme in complex differential geometry is to find a correspondence between algebraic objects and differential geometric objects. One of the most attractive is the non-abelian Hodge theory of Simpson. In this paper, pursuing an analogue of the non-abelian Hodge theory in the context of $q$-difference modules, we study Kobayashi-Hitchin correspondences between doubly periodic monopoles and parabolic $q$-difference modules, depending on twistor parameters.

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Takuro Mochizuki. 2019-02-10. Doubly periodic monopoles and $q$-difference modules. https://arxiv.org/abs/1902.03551

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