Moduli of Double Epw-sextics

The author studies the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of $bigwedge3mathbb C6$ modulo the natural action of $mathrmSL6$, call it $mathfrakM$. 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.