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J. Korean Math. Soc. 2024; 61(1): 161-181

Online first article December 21, 2023      Printed January 1, 2024

https://doi.org/10.4134/JKMS.j230278

Copyright © The Korean Mathematical Society.

Geometry of the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one

Sang-Bum Yoo

Gongju National University of Education

Abstract

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We describe the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one and its geometric structures in terms of the Hitchin map and a flat degeneration of the moduli space of Higgs bundles on an elliptic curve.

Keywords: Higgs pair, generalized parabolic Higgs bundle, Gieseker-Hitchin pair, Hitchin map, flat degeneration, irreducible nodal curve of arithmetic genus one

MSC numbers: Primary 14D06, 14D20, 14D22, 14E05, 14H10, 14H52

Supported by: This work was supported by the National Research Foundation of Korea grant funded by the Korea government(MSIT) (No. 2021R1F1A1062436).

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