Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

Mochizuki, Takuro

doi:10.3842/sigma.2021.068

Cited by 5 publications

(3 citation statements)

References 66 publications

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“…Note that i∈S(P ) h t,P,i and h t|X * P are mutually bounded for any P ∈ D. Hence, Tr(s t ) is bounded. We also note the following vanishing (see Lemma [17,Lemma 4.7]):…”

Section: The Case Of Locally and Globally Irreducible Higgs Bundlesmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic behaviour of large-scale solutions of Hitchin's equations in higher rank

Mochizuki¹,

Szabó²

2023

Preprint

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Let X be a compact Riemann surface. Let (E, θ) be a stable Higgs bundle of degree 0 on X. Let h det(E) denote a flat metric of the determinant bundle det(E). For any t > 0, there exists a unique harmonic metric ht of (E, θ) such that det(ht) = h det(E) . We prove that if the Higgs bundle is induced by a line bundle on the normalization of the spectral curve, then the sequence ht is convergent to the naturally defined decoupled harmonic metric at the speed of the exponential order. We also obtain a uniform convergence for such a family of Higgs bundles.

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“…Note that i∈S(P ) h t,P,i and h t|X * P are mutually bounded for any P ∈ D. Hence, Tr(s t ) is bounded. We also note the following vanishing (see Lemma [17,Lemma 4.7]):…”

Section: The Case Of Locally and Globally Irreducible Higgs Bundlesmentioning

confidence: 99%

“…Conversely, let (P * V, θ) be a polystable decomposable filtered Higgs bundle of degree 0 on (X, D) such that (V, θ) = (V, θ) |X\D is regular semisimple. There exists a harmonic metric h of (V, θ) adapted to P * V by [2,17,19]. Proposition 5.34 h is a decoupled harmonic metric.…”

Section: Kobayashi-hitchin Correspondence For Decoupled Harmonic Bundlesmentioning

confidence: 99%

Asymptotic behaviour of large-scale solutions of Hitchin's equations in higher rank

Mochizuki¹,

Szabó²

2023

Preprint

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show abstract

“…We assume that X is compact. Recall that for any filtered bundle P * V on (X, D), we obtain deg(P * V) ∈ R as follows (see [13,14] and also [12]):…”

Section: Compact Casementioning

confidence: 99%

Harmonic metrics of generically regular semisimple Higgs bundles on non-compact Riemann surfaces

Li¹,

Mochizuki²

2022

Preprint

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We prove that a generically regular semisimple Higgs bundle equipped with a non-degenerate symmetric pairing on any Riemann surface always has a harmonic metric compatible with the pairing. We also study the classification of such compatible harmonic metrics in the case where the Riemann surface is the complement of a finite set D in a compact Riemann surface. In particular, we prove the uniqueness of a compatible harmonic metric if the Higgs bundle is wild and regular semisimple at each point of D.

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The Hitchin-Kobayashi correspondence on twisted λ-flat bundles

Pan

2022

Bulletin des Sciences Mathématiques

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Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

Cited by 5 publications

References 66 publications

Asymptotic behaviour of large-scale solutions of Hitchin's equations in higher rank

Asymptotic behaviour of large-scale solutions of Hitchin's equations in higher rank

Harmonic metrics of generically regular semisimple Higgs bundles on non-compact Riemann surfaces

The Hitchin-Kobayashi correspondence on twisted λ-flat bundles

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