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The writer stories the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of $\bigwedge^3{\mathbb C}^6$ modulo the typical motion of $\mathrm{SL}_6$, name it $\mathfrak{M}$. it is a compactification of the moduli house of gentle double EPW-sextics and for this reason birational to the moduli area of HK $4$-folds of variety $K3^{[2]}$ polarized by way of a divisor of sq. $2$ for the Beauville-Bogomolov quadratic shape. the writer will ensure the reliable issues. His paintings bears a robust analogy with the paintings of Voisin, Laza and Looijenga on moduli and sessions of cubic $4$-folds.

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