In
algebraic geometry
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
, a line complex is a 3-fold given by the intersection of the Grassmannian ''G''(2, 4) (embedded in projective space ''P''
5 by
Plücker coordinates) with a hypersurface. It is called a line complex because points of ''G''(2, 4) correspond to lines in ''P''
3, so a line complex can be thought of as a 3-dimensional family of lines in ''P''
3. The linear line complex and quadric line complex are the cases when the hypersurface has degree 1 or 2; they are both
rational varieties.
References
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Algebraic varieties
3-folds
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