The Hitchin fibration under degenerations to noded Riemann surfaces

2016/09/16 by Jan Swoboda, Swoboda, Jan
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Advanced Operator Algebra Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1609.04928

Abstract

In this note we study some analytic properties of the linearized self-duality equations on a family of smooth Riemann surfaces Σ_R converging for R\searrow0 to a surface Σ₀ with a finite number of nodes. It is shown that the linearization along the fibres of the Hitchin fibration gives rise to a graph-continuous Fredholm family, the index of it being stable when passing to the limit. We also report on similarities and differences between properties of the Hitchin fibration in this degeneration and in the limit of large Higgs fields.

Citations

• The Self-Duality Equations on a Riemann Surface

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