Periodicity of Hitchin's uniformizing Higgs bundles
Raju Krishnamoorthy, Mao Sheng
TL;DR
This paper explores the periodicity of Hitchin's uniformizing Higgs bundles and connects it with the arithmetic geometry of the underlying curve, revealing new relations and speculating on the broader class of such bundles.
Contribution
It establishes a novel link between Higgs bundle periodicity and arithmetic geometry, and proposes new relations and conjectures about periodic Higgs bundles.
Findings
Discovered new relations between Higgs bundle periodicity and arithmetic geometry.
Linked the periodicity of Hitchin's bundles to properties of the underlying curve.
Speculated on the classification of all periodic Higgs bundles.
Abstract
We link the periodicity of Hitchin's uniformizing Higgs bundle with the arithmetic geometry of its underlying curve. Some new relations are discovered. We also speculate on the whole class of periodic Higgs bundles.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry