Moduli spaces of Lambda-modules on abelian varieties

Author(s)

Franco, Emilio ; Tortella, Pietro

• Document type: Journal article
• Source: ADVANCES IN MATHEMATICS; v. 318, p. 459-496, OCT 1 2017.
• Web of Science Citations: 0

Abstract

We study the moduli space M-x (Lambda, n) of semistable Lambda-modules of vanishing Chern classes over an abelian variety X, where A belongs to a certain subclass of D-algebras. In particular, for Lambda = D-X (resp. A = Sym(center dot)TX) we obtain a description of the moduli spaces of flat connections (resp. Higgs bundles). We give a description of M-x (Lambda, n) in terms of a symmetric product of a certain fibre bundle over the dual abelian variety (X) over cap. We also give a moduli interpretation to the associated Hilbert scheme as the classifying space of Lambda-modules with extra structure. Finally, we study the non-abelian Hodge theory associated to these new moduli spaces. (C) 2017 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 15/06696-2 - Behavior of branes under mirror symmetry in the moduli spaces of Higgs bundles
• Grantee: Emilio Franco Gómez
• Support type: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 11/17593-9 - Holomorphic Lie algebroids, stacks of twisted modules and applications to the Hitchin system and Poisson geometry.
• Grantee: Pietro Tortella
• Support type: Scholarships in Brazil - Post-Doctorate
• FAPESP's process: 12/16356-6 - Higgs bundles over elliptic curves
• Grantee: Emilio Franco Gómez
• Support type: Scholarships in Brazil - Post-Doctorate