# A weight two phenomenon for the moduli of rank one local systems on open varieties

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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https://hal.archives-ouvertes.fr/hal-00179373
Contributor : Carlos Simpson <>
Submitted on : Monday, October 15, 2007 - 2:05:33 PM
Last modification on : Friday, January 12, 2018 - 1:51:26 AM
Long-term archiving on: Sunday, April 11, 2010 - 11:01:50 PM

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• HAL Id : hal-00179373, version 1
• ARXIV : 0710.2800

### Citation

Carlos Simpson. A weight two phenomenon for the moduli of rank one local systems on open varieties. 2007. ⟨hal-00179373⟩

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