Higgs bundles over elliptic curves

• Grant number: 12/16356-6
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2013
• End date: December 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Marcos Benevenuto Jardim
• Grantee: Emilio Franco Gómez
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 15/06696-2 - Behavior of branes under mirror symmetry in the moduli spaces of Higgs bundles, BE.EP.PD

Abstract

This project is divided in two parts. First, we continue the aplicants PhD project studying the moduli spaces of principal bundles over elliptic curves, providing explicit descriptions of such moduli spaces. At the same time, we study the Fourier-Mukai transform of Q-bundles and parabolic Higgs bundles over projective varieties, especially over elliptic curves.

Scientific publications

(6)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

FRANCO, EMILIO; JARDIM, MARCOS; MENET, GREGOIRE. Brane involutions on irreducible holomorphic symplectic manifolds. KYOTO JOURNAL OF MATHEMATICS, v. 59, n. 1, p. 195-235, APR 2019. (14/05733-9, 15/06696-2, 12/16356-6, 16/03759-6)

FRANCO, EMILIO; GARCIA-PRADA, OSCAR; NEWSTEAD, P. E.. HIGGS BUNDLES OVER ELLIPTIC CURVES FOR REAL GROUPS. QUARTERLY JOURNAL OF MATHEMATICS, v. 70, n. 1, p. 105-146, MAR 2019. (15/06696-2, 12/16356-6)

FRANCO, EMILIO; JARDIM, MARCOS; MARCHESI, SIMONE. Branes in the moduli space of framed sheaves. BULLETIN DES SCIENCES MATHEMATIQUES, v. 141, n. 4, p. 353-383, JUN 2017. (12/16356-6, 15/06696-2, 14/14743-8, 14/19676-7)

FRANCO, EMILIO; TORTELLA, PIETRO. Moduli spaces of Lambda-modules on abelian varieties. ADVANCES IN MATHEMATICS, v. 318, p. 459-496, OCT 1 2017. (15/06696-2, 11/17593-9, 12/16356-6)

FRANCO, EMILIO; JARDIM, MARCOS. Mirror symmetry for Nahm branes. EPIJOURNAL DE GEOMETRIE ALGEBRIQUE, v. 6, p. 29-pg., 2022-02-28. (12/16356-6, 16/03759-6, 18/21391-1)

BISWAS, INDRANIL; ANGEL CALVO, LUIS; FRANCO, EMILIO; GARCIA-PRADA, OSCAR. Involutions of Higgs moduli spaces over elliptic curves and pseudo-real Higgs bundles. JOURNAL OF GEOMETRY AND PHYSICS, v. 142, p. 47-65, AUG 2019. (15/06696-2, 12/16356-6)