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We study moduli spaces of O'Grady's ten-dimensional irreducible symplecticmanifolds. These moduli spaces are covers of modular varieties of dimension 21,namely quotients of hermitian symmetric domains by a suitable arithmetic group.The interesting and new aspect of this case is that the group in question isstrictly bigger than the stable orthogonal group. This makes it different fromboth the K3 and the K3^[n] case, which are of dimension 19 and 20 respectively.

Moduli spaces of polarised symplectic O'Grady varieties and Borcherds products