Lattice polarized irreducible holomorphic symplectic manifolds

Camere, Chiara

Annales de l'Institut Fourier, Tome 66 (2016) no. 2, pp. 687-709.

On généralise la construction de la symétrie miroir des surfaces K3 aux variétés irréductibles holomorphes symplectiques $X$ polarisées par un réseau. Dans le cas des variétés de type $K{3}^{\left[2\right]}$ on étudie la famille miroir des variétés polarisées et on généralise la notion de couple d’involutions non-symplectiques miroirs.

We generalize 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.

Classification : 14J15, 32G13, 14J33, 14J35
Keywords: lattice polarized irreducible holomorphic symplectic manifold, mirror symmetry, lattice polarized hyperkähler manifold, mirror involution
Mot clés : variété irréductible holomorphe symplectique polarisée par un réseau, symétrie miroir, variété hyperkählerienne polarisée par un réseau, involution miroir

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