The derived moduli stack of logarithmic flat connections

Francis Bischoff

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arXiv · 2301.00962

The derived moduli stack of logarithmic flat connections

Francis Bischoff

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Abstract

We give an explicit finite-dimensional model for the derived moduli stack of flat connections on $\mathbb{C}^k$ with logarithmic singularities along a weighted homogeneous Saito free divisor. We investigate in detail the case of plane curves of the form $x^p = y^q$ and relate the moduli spaces to the Grothendieck-Springer resolution. We also discuss the shifted Poisson geometry of these moduli spaces. Namely, we conjecture that the map restricting a logarithmic connection to the complement of the divisor admits a shifted coisotropic structure and we construct a shifted Poisson structure on the formal neighborhood of a canonical connection in the case of plane curves $x^p = y^q$.

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Francis Bischoff. 2023-01-03. The derived moduli stack of logarithmic flat connections. https://arxiv.org/abs/2301.00962

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