A survey of non-Abelian Hodge theory and related moduli spaces, with a new explicit description of Simpson filtrations for rank 3 flat bundles.
A weight two phenomenon for the moduli of rank one local systems on open varieties
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abstract
The twistor space of representations on an open variety maps to a weight two space of local monodromy transformations around a divisor component at infinty. The space of $\sigma$-invariant sections of this slope-two bundle over the twistor line is a real 3 dimensional space whose parameters correspond to the complex residue of the Higgs field, and the real parabolic weight of a harmonic bundle.
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Non-Abelian Hodge Theory and Related Topics
A survey of non-Abelian Hodge theory and related moduli spaces, with a new explicit description of Simpson filtrations for rank 3 flat bundles.