Moduli spaces of quadratic complexes and their singular surfaces

Abstract

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