Unramified covers and branes on the Hitchin system

• Type: Article in International Scientific Journal
• Date: 2021

Authors

André Oliveira (Author) FCUP; Gothen, PB (Author) FCUP; Emilio Franco (Author) Other; Ana Peon-Nieto (Author) Other

Journal

Title: Advances in Mathematics

Vol. 377

ISSN: 0001-8708

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 8 Citations

Other information

Authenticus ID: P-00T-2ZA

DOI: 10.1016/j.aim.2020.107493

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 61