Unramified covers and branes on the Hitchin system

• Autor(es): André Oliveira ; Gothen, PB ; Emilio Franco ; Ana Peon-Nieto
• Data: 2021
• Identificador Persistente: https://hdl.handle.net/10216/130402
• Origem: Repositório Aberto da Universidade do Porto
• Tipo de Documento: Artigo científico
• Idioma: Inglês

Descrição

We study the locus of the moduli space of GL(n, C)-Higgs bundles on a curve given by those Higgs bundles obtained by pushforward under a connected unramified cover. We equip these loci with a hyperholomorphic bundle so that they can be viewed as BBB-branes, and we introduce corresponding BAA-branes which can be described via Hecke modifications. We then show how these branes are naturally dual via explicit Fourier-Mukai transform (recall that GL(n, C) is Langlands self dual). It is noteworthy that these branes lie over the singular locus of the Hitchin fibration. As a particular case, our construction describes the behavior under mirror symmetry of the fixed loci for the action of tensorization by a line bundle of order n. These loci play a key role in the work of Hausel and Thaddeus on topological mirror symmetry for Higgs moduli spaces. (C) 2020 Published by Elsevier Inc.