Moduli of double EPW-sextics

The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of \bigwedge^3{\mathbb C}^6 modulo the natural action of \mathrm{SL}_6, call it \mathfrak{M}. This is a compactification of the moduli space of smooth double EPW-sextics and hence birational to the moduli space of HK 4-folds of Type K3^{[2]} polarized by a divisor of square 2 for the Beauville-Bogomolov quadratic form. The author will determine the stable points. His work bears a strong analogy with the work of Voisin, Laza and Looijenga on moduli and periods of cubic 4-folds.