- Examples
- References
In algebraic geometry, a cubic threefold is a hypersurface of degree 3 in 4-dimensional projective space. Cubic threefolds are all unirational, but {{harvtxt|Clemens|Griffiths|1972}} used intermediate Jacobians to show that non-singular cubic threefolds are not rational. The space of lines on a non-singular cubic 3-fold is a Fano surface. Examples- Koras–Russell cubic threefold
- Klein cubic threefold
- Segre cubic
References- {{Citation | last1=Bombieri | first1=Enrico | author1-link=Enrico Bombieri | last2=Swinnerton-Dyer | first2=H. P. F. | author2-link=Peter Swinnerton-Dyer | title=On the local zeta function of a cubic threefold | url=http://www.numdam.org/item?id=ASNSP_1967_3_21_1_1_0 | mr=0212019 | year=1967 | journal=Ann. Scuola Norm. Sup. Pisa (3) | volume=21 | pages=1–29}}
- {{Citation | last1=Clemens | first1=C. Herbert | last2=Griffiths | first2=Phillip A. | title=The intermediate Jacobian of the cubic threefold | jstor=1970801 | mr=0302652 | year=1972 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=95 | issue=2 | pages=281–356 | doi=10.2307/1970801| citeseerx=10.1.1.401.4550 }}
- {{Citation | last1=Murre | first1=J. P. | title=Algebraic equivalence modulo rational equivalence on a cubic threefold | url=http://www.numdam.org/item?id=CM_1972__25_2_161_0 | mr=0352088 | year=1972 | journal=Compositio Mathematica | issn=0010-437X | volume=25 | pages=161–206}}
2 : Algebraic varieties|3-folds |