Brane involutions on irreducible holomorphic symplectic manifolds

Autor(es)

Franco, Emilio ^[1] ; Jardim, Marcos ^[2] ; Menet, Gregoire ^[3]

Afiliação do(s) autor(es)

^[1] Univ Porto, Fac Ciencias, Ctr Matemat, Porto - Portugal

^[2] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil

^[3] Univ Grenoble, Inst Fourier, St Martin Dheres - France

• Tipo de documento: Artigo Científico
• Fonte: KYOTO JOURNAL OF MATHEMATICS; v. 59, n. 1, p. 195-235, APR 2019.
• Citações Web of Science: 0

Resumo

In the context of irreducible holomorphic symplectic manifolds, we say that (anti)holomorphic (anti)symplectic involutions are brane involutions since their fixed point locus is a brane in the physicists' language, that is, a submanifold which is either a complex or Lagrangian submanifold with respect to each of the three Kahler structures of the associated hyper-Kahler structure. Starting from a brane involution on a K3 or Abelian surface, one can construct a natural brane involution on its moduli space of sheaves. We study these natural involutions and their relation with the Fourier-Mukai transform. Later, we recall the lattice-theoretical approach to mirror symmetry. We provide two ways of obtaining a brane involution on the mirror, and we study the behavior of the brane involutions under both mirror transformations, giving examples in the case of a K3 surface and K3({[}2]) -type manifolds. (AU)

• Processo FAPESP: 14/05733-9 - Geometria de variedades simpléticas irredutíveis
• Beneficiário: Grégoire Menet
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 15/06696-2 - Comportamento das branas sob a transformação da simetria espelho no espaço de moduli de fibrados de Higgs
• Beneficiário: Emilio Franco Gómez
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 12/16356-6 - Fibrados de Higgs sobre curvas elípticas
• Beneficiário: Emilio Franco Gómez
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 16/03759-6 - Espaços de módulos de feixes no espaço projetivo
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Bolsas no Exterior - Pesquisa