Moduli and periods of double EPW-sextics

We analyze the GIT-quotient of the symplectic grassmannian parametrizing lagrangian subspaces of $\bigwedge3{\mathbb C}6$ modulo PGL(6) - a compactification of the moduli space of double EPW-sextics. The family of double EPW-sextics is similar to the family of cubic 4-folds. Our final goal will be to analyze the period map from the GIT-quotient to the Baily-Borel compactification of the relevant bounded symmetric domain. We are inspired by the works of C.Voisin, B. Hassett, R.Laza and E. Looijenga on periods of cubic 4-folds.