Abstract
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.
Citation
Emilio Franco. Marcos Jardim. Grégoire Menet. "Brane involutions on irreducible holomorphic symplectic manifolds." Kyoto J. Math. 59 (1) 195 - 235, April 2019. https://doi.org/10.1215/21562261-2018-0009
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