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Moduli spaces of quadratic complexes and their singular surfaces

Authors:	Dan Avritzer Herbert Lange

Institution:	1.Departamento de Matemática,UFMG,Belo Horizonte,Brazil;2.Mathematisches Institut,Friedrich-Alexander-Universit?t Erlangen-Nürnberg,Erlangen,Germany

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

Keywords:	Moduli spaces Quadratic complexes Segre symbols Quadrics
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