Non-abelian Hodge theory and moduli spaces of Higgs bundles

 

Enregistré dans:
Détails bibliographiques
Auteur: Gallego , Guillermo
Format: artículo original
Statut:Versión publicada
Date de publication:2026
Description:This paper provides an introduction to non-abelian Hodge theory and moduli spaces of Higgs bundles on compact Riemann surfaces. We develop the moduli theory of vector bundles and Higgs bundles, establish the main correspondences of non-abelian Hodge theory, and interpret them through the hyperkähler structure on the Hitchin moduli space. We study the Hitchin fibration and its geometric properties, including SYZ mirror symmetry and topological mirror symmetry for type A Hitchin systems. As an illustration, we compute the Poincaré polynomial of the rank 2 moduli space and verify topological mirror symmetry in this case.
Pays:Portal de Revistas UCR
Institution:Universidad de Costa Rica
Repositorio:Portal de Revistas UCR
Langue:Inglés
OAI Identifier:oai:portal.revistas.ucr.ac.cr:article/4610
Accès en ligne:https://revistas.ucr.ac.cr/index.php/rmatematica/article/view/4610
Mots-clés:Higgs bundles
Non-abelian Hodge theory
Hitchin fibration
Fibrados de Higgs
Teoría de Hodge No-abeliana
Fibración de Hitchin