Moduli spaces of quadratic complexes and their singular surfaces.

The aim of this talk is to construct the coarse moduli space $cM_{qc}(sigma)$ of quadratic line complexes with a fixed Segre symbol $sigma$ as well as the moduli space $cM_{ss}(sigma)$ of the corresponding singular surfaces. We show that the map associating to a quadratic line complex its singular surface induces a morphism $pi: cM_{qc}(sigma)
a cM_{ss}(sigma)$. Finally we deduce that the varieties of cosingular quadratic line complexes are almost always curves.