Monodromy of Rank 2 Parabolic Hitchin Systems
Georgios Kydonakis, Hao Sun, Lutian Zhao
TL;DR
This paper investigates the monodromy of the Hitchin fibration for moduli spaces of parabolic G-Higgs bundles with G=SL(2,R), GL(2,R), and PGL(2,R), providing an exact count of components via monodromy orbits.
Contribution
It offers a detailed calculation of monodromy orbits with Z2-coefficients, leading to precise component counts for these moduli spaces.
Findings
Monodromy orbits are explicitly computed for the specified groups.
The number of components of the moduli spaces is exactly determined.
The approach enhances understanding of the topology of parabolic Higgs bundle moduli spaces.
Abstract
We study the monodromy of the Hitchin fibration for moduli spaces of parabolic G-Higgs bundles in the cases when G=SL(2,R), GL(2,R) and PGL(2,R) A calculation of the orbits of the monodromy with Z2-coefficients provides an exact count of the components of the moduli spaces for these groups.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Geometry and complex manifolds