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 Plücker 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
- {{Citation | last1=Griffiths | first1=Phillip | author1-link=Phillip Griffiths | last2=Harris | first2=Joseph | author2-link=Joe Harris (mathematician) | title=Principles of algebraic geometry | publisher=John Wiley & Sons | location=New York | series=Wiley Classics Library | isbn=978-0-471-05059-9 |mr=1288523 | year=1994}}
- {{Citation | last1=Jessop | first1=C. M. | title=A treatise on the line complex | orig-year=1903 | url=http://digital.library.cornell.edu/cgi/t/text/text-idx?c=math;idno=06960001 | publisher=American Mathematical Society | location=Providence, R.I. | isbn=978-0-8218-2913-4 |mr=0247995 | year=2001}}
- {{Citation | last1=Klein | first1=Felix | title= Zur Theorie der Liniencomplexe des ersten und zweiten Grades | publisher=Springer Berlin / Heidelberg | doi=10.1007/BF01444020 | year=1870 | journal=Mathematische Annalen | issn=0025-5831 | volume=2 | issue=2 | pages=198–226| s2cid=121706710 | url=https://zenodo.org/record/1607513 }}
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