Remarks on Higgs bundles twisted by a vector bundle

D. Alfaya, I. Biswas, P. Kumar

International Journal of Mathematics Vol. 37, nº. 9, pp. 2650041

Summary:

For any V-twisted Higgs bundle on a compact connected Riemann surface X, where V is a holomorphic vector bundle of rank two over X, there are two associated Higgs bundles on X, twisted by line bundles, which are constructed using a Hecke transformation on V. We characterize all such pairs of Higgs bundles (twisted by line bundles) given by the V-twisted Higgs bundles. Using this characterization, we provide a spectral correspondence for the moduli space, identifying V-twisted Higgs bundles with the direct images of certain rank one torsionfree Higgs sheaves twisted by a line bundle on a spectral covering of the curve X.

Spanish layman's summary:

Utilizando transformaciones de Hecke, proporcionamos una correspondencia espectral para los espacios de moduli de fibrados de Higgs retorcidos por un fibrado vectorial de rango 2.

English layman's summary:

Using Hecke transformations, we develop a spectral correspondence for moduli spaces of Higgs bundles twisted by a rank 2 vector bundle.

Keywords: Twisted Higgs bundle; Hecke transformation; spectral curve; Fibrado de Higgs retorcido, transformación de Hecke, curva espectral.

JCR-JIF Impact Factor and WoS quartile: 0,600 - Q3 (2025)

DOI reference: https://doi.org/10.1142/S0129167X26500412

Published on paper: August 2026.

Published on-line: April 2026.

Citation:
D. Alfaya, I. Biswas, P. Kumar, "Remarks on Higgs bundles twisted by a vector bundle", International Journal of Mathematics, Vol. 37, nº. 9, pp. 2650041, August 2026. [Online: April 2026] doi: 10.1142/S0129167X26500412