Moduli spaces of Higgs bundles on degenerating Riemann surfaces

We prove a gluing theorem for solutions (A0,Φ0) of Hitchin's self-duality equations with logarithmic singularities on a rank-2 vector bundle over a noded Riemann surface Σ0 representing a boundary point of Teichmüller moduli space. We show that every nearby smooth Riemann surface Σ1 carries a s...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2017-12, Vol.322, p.637-681, Article 637
Main Author: Swoboda, Jan
Format: Article
Language:English
Subjects:
Cappell–Lee–Miller gluing theorem
Dirac-type operators on manifolds with cylindrical ends
Higgs bundles
Moduli spaces
Noded Riemann surfaces
Self-duality equations
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Summary:We prove a gluing theorem for solutions (A0,Φ0) of Hitchin's self-duality equations with logarithmic singularities on a rank-2 vector bundle over a noded Riemann surface Σ0 representing a boundary point of Teichmüller moduli space. We show that every nearby smooth Riemann surface Σ1 carries a smooth solution (A1,Φ1) of the self-duality equations, which may be viewed as a desingularization of (A0,Φ0).
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2017.10.028