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Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Wednesday, July 14, 14:00 ~ 14:40 UTC-3

Moduli varieties of twisted local systems

Florent Schaffhauser

Universidad de Los Andes, Colombia   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Complex analytic orbi-curves give rise to natural examples of twisted local systems, for which the fundamental group acts non-trivially on the coefficients. In this talk, we construct moduli varieties of twisted local systems, and prove that these are affine varieties over the complex numbers, whose (strong) topology can be studied through an appropriate generalization of the non-Abelian Hodge correspondence to the case of nonconstant coefficients. This partially answers a question of Carlos Simpson on the meaning of the Dolbeault moduli space in the nonconstant case.

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