# Quadratic complexes, singular varieties and moduli

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Let G be the Grassmannian of lines in P3 embedded in P5 as the Plücker quadric Q. The intersection of Q with a second hypersurface of degree d is what is called a complex of lines of degree d. When we consider the intersection of Q with a second quadratic hypersurface in P5, P, we have a quadratic complex. Let X = Q ∩ P be a quadratic complex that, in this talk, we assume to be non-singular, meaning X is non-singular.