Segre cubic [SEP] named after
Segre cubic
In algebraic geometry, the Segre cubic is a cubic threefold embedded in 4 (or sometimes 5) dimensional projective space, studied by .
The Segre cubic is the set of points ("x":"x":"x":"x":"x":"x") of "P" satisfying the equations
Its intersection with any hyperplane "x" = 0 is the Clebsch cubic surface. Its intersection with any hyperplane "x" = "x" is Cayley's nodal cubic surface. Its dual is the Igusa quartic 3-fold in P. Its Hessian is the Barth
Z)-action on the space of integral binary cubic forms and cubic rings up to isomorphism.
The classification of real cubic forms formula_1 is linked to the classification of umbilical points of surfaces. The equivalence classes of such cubics form a three-dimensional real projective space and the subset of parabolic forms define a surface – the umbilic torus.
Examples.
- Cubic plane curve
- Elliptic curve
- Fermat cubic
- Cubic 3-fold
- Koras–Russell cubic threefold
- Klein cubic threefold
- Segre cubic