Spectral Coverings without Embeddings

C. R. Math. Rep. Acad. Sci. Canada Vol. 47 (2) 2025, pp. 10–20
(Received: 2025-07-15 , Revised: 2025-07-24)

Eric Boulter, Department of Mathematics and Statistics, University of Saskatchewan, SK, Canada S7N 5E6; email: eric.boulter@usask.ca

Steven Rayan, Centre for Quantum Topology and Its Applications (quanTA) and Department of
Mathematics and Statistics, University of Saskatchewan, SK, Canada S7N 5E6; e-mail: rayan@math.usask.ca

Abstract/Résumé:

In this article, we investigate a weakened version of the spectral correspondence for twisted Higgs bundles. Namely, we construct twisted Higgs bundles from a finite covering map and a vector bundle on that covering but without requiring that they match the eigen-data for some fixed twisted Higgs bundle. We investigate stability for twisted Higgs bundles constructed in this way, and compare our covering data to that of the traditional spectral cover.

Dans cet article, nous étudions une version affaiblie de la correspondance spectrale pour les fibrés de Higgs torsadés. Nous construisons des fibrés de Higgs torsadés à partir d’une application de couverture finie et d’un fibré vectoriel sur cette couverture, sans exiger qu’ils correspondent aux données propres d’un fibré de Higgs torsadé fixe. Nous étudions la stabilité des fibrés de Higgs torsadés ainsi construits et comparons nos données de couverture à celles de la couverture spectrale traditionnelle.

Keywords: Higgs bundle, Spectral correspondence, covering map, normalization, spectral cover, spectral curve, stability, twisted Higgs bundle

AMS Subject Classification: Algebraic moduli problems; moduli of vector bundles, , Special curves and curves of low genus, Vector bundles on surfaces and higher-dimensional varieties; and their moduli, Curves, Higher-dimensional varieties 14D20, 14F06, 14H45, 14J60, 14Q05, 14Q15

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