Line complex
In algebraic geometry, a line complex is a 3-fold given by the intersection of the Grassmannian G(2,4) (embedded in projective space P5 by Plucker coordinates) with a hypersurface. It is called a line complex because points of G(2,4) correspond to lines in P3, so a line complex can be thought of as a 3-dimensional family of lines in P3. 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
- Griffiths, Phillip; Harris, Joseph (1994), Principles of algebraic geometry, Wiley Classics Library, New York: John Wiley & Sons, ISBN 978-0-471-05059-9, MR1288523
- Jessop, C. M. (1969), A treatise on the line complex, New York: Chelsea Publishing Co., MR0247995
- Klein, Felix (1870), "Zur Theorie der Liniencomplexe des ersten und zweiten Grades", Mathematische Annalen, 2 (2), Springer Berlin / Heidelberg: 198–226, doi:10.1007/BF01444020, ISSN 0025-5831