Lattice polarized irreducible holomorphic symplectic manifolds

Abstract

We generalize Nikulin's and Dolgachev's lattice-theoretical mirror symmetry for K3 surfaces to lattice polarized higher dimensional irreducible holomorphic symplectic manifolds. In the case of fourfolds of $K{3}^{\left[2\right]}-$type we then describe mirror families of polarized fourfolds and we give an example with mirror non-symplectic involutions.

Comments are welcome

Cited by in corpus (4)

• Classification of automorphisms on a deformation family of hyperkähler fourfolds by p-elementary lattices
• Tautological classes on moduli space of hyperkähler manifolds
• Moduli Spaces of Symmetric Cubic Fourfolds and Locally Symmetric Varieties
• Brane involutions on irreducible holomorphic symplectic manifolds