Normal forms and moduli stacks for logarithmic flat connections

Bischoff, Francis

doi:10.1090/jag/837

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Normal forms and moduli stacks for logarithmic flat connections

Author: Francis Bischoff
Journal: J. Algebraic Geom.
DOI: https://doi.org/10.1090/jag/837
Published electronically: September 13, 2024
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Abstract: We establish normal form theorems for a large class of singular flat connections on complex manifolds, including connections with logarithmic poles along weighted homogeneous Saito free divisors. As a result, we show that the moduli spaces of such connections admit the structure of algebraic quotient stacks. In order to prove these results, we introduce homogeneous Lie groupoids and study their representation theory. In this direction, we prove two main results: a Jordan–Chevalley decomposition theorem and a linearization theorem. We give explicit normal forms for several examples of free divisors, such as homogeneous plane curves, reductive free divisors, and one of Sekiguchi’s free divisors.

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Additional Information

Francis Bischoff
Affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK
Address at time of publication: Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S 0A2, Canada
MR Author ID: 1396134
ORCID: 0000-0001-6995-5911
Email: Francis.Bischoff@uregina.ca

Received by editor(s): February 6, 2023
Received by editor(s) in revised form: February 21, 2024, and May 30, 2024
Published electronically: September 13, 2024
Article copyright: © Copyright 2024 University Press, Inc.

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