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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Brane involutions on irreducible holomorphic symplectic manifolds

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Franco, Emilio [1] ; Jardim, Marcos [2] ; Menet, Gregoire [3]
Total Authors: 3
[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
Total Affiliations: 3
Document type: Journal article
Source: KYOTO JOURNAL OF MATHEMATICS; v. 59, n. 1, p. 195-235, APR 2019.
Web of Science Citations: 0

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)

FAPESP's process: 14/05733-9 - Geometry of irreducible symplectic varieties
Grantee:Grégoire Menet
Support Opportunities: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 15/06696-2 - Behavior of branes under mirror symmetry in the moduli spaces of Higgs bundles
Grantee:Emilio Franco Gómez
Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
FAPESP's process: 12/16356-6 - Higgs bundles over elliptic curves
Grantee:Emilio Franco Gómez
Support Opportunities: Scholarships in Brazil - Post-Doctorate
FAPESP's process: 16/03759-6 - Moduli spaces of stable objects on the projective space
Grantee:Marcos Benevenuto Jardim
Support Opportunities: Scholarships abroad - Research