Line complex

In algebraic geometry, a line complex is a set of lines that can be specified by a list of homogeneous polynomial equations. That is, a projective variety of lines.

A linear line complex is defined by a list of degree-1 polynomials. A quadratic line complex is defined by a list of degree-2 polynomials. Similarly for cubic, quartic, quintic, sextic, etc.

They were first studied by Julius Plücker in Neue Geometrie des Raumes (1868). Other important figures include Felix Klein, Sophus Lie, Arthur Cayley, William Hamilton, and Alfred Clebsch.

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