Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 59, Number 1 (2019), 195-235.
Brane involutions on irreducible holomorphic symplectic manifolds
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 Kähler structures of the associated hyper-Kähler structure. Starting from a brane involution on a 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 surface and -type manifolds.
Kyoto J. Math., Volume 59, Number 1 (2019), 195-235.
Received: 5 July 2016
Accepted: 10 February 2017
First available in Project Euclid: 8 January 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Franco, Emilio; Jardim, Marcos; Menet, Grégoire. Brane involutions on irreducible holomorphic symplectic manifolds. Kyoto J. Math. 59 (2019), no. 1, 195--235. doi:10.1215/21562261-2018-0009. https://projecteuclid.org/euclid.kjm/1546916422