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<p>The moduli space of stable Higgs bundles of degree 0 is equipped with the hyperkähler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperkähler metric called the semi-flat metric, associated with the algebraic integrable systems with the Hitchin section. We prove the exponentially rapid decay of the difference between the Hitchin metric and the semi-flat metric along the ray <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mo stretchy="false">(</mo> <mi>E</mi> <mo>,</mo> <mi>t</mi> <mi>θ</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$(E,t\theta )$</EquationSource> </InlineEquation> as <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>t</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </math></EquationSource> <EquationSource Format="TEX">$t\to \infty $</EquationSource> </InlineEquation>.</p>

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Asymptotic Behaviour of the Hitchin Metric on the Moduli Space of Higgs Bundles

  • 期刊论文

  • 发表日期：

    2026年4月14日

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  • Takuro Mochizuki

摘要

The moduli space of stable Higgs bundles of degree 0 is equipped with the hyperkähler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperkähler metric called the semi-flat metric, associated with the algebraic integrable systems with the Hitchin section. We prove the exponentially rapid decay of the difference between the Hitchin metric and the semi-flat metric along the ray ( E , t θ ) $(E,t\theta )$ as t → ∞ $t\to \infty $ .