Barth–Nieto quintic
Encyclopedia
In algebraic geometry, the Barth–Nieto quintic is a quintic 3-fold in 4 (or sometimes 5) dimensional projective space studied by that is the Hessian of the Segre cubic
. The Barth–Nieto quintic is the closure of the set of points (x0:x1:x2:x3:x4:x5) of P5 satisfying the equations
The Barth–Nieto quintic is not rational, but has a smooth model that is a Calabi-Yau manifold
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Segre cubic
In algebraic geometry, the Segre cubic is a cubic threefold embedded in 4 dimensional projective space, studied by .The Segre cubic is the set of points of P5 satisfying the equations\displaystyle x_0+x_1+x_2+x_3+x_4+x_5= 0\displaystyle x_0^3+x_1^3+x_2^3+x_3^3+x_4^3+x_5^3 = 0.Its intersection...
. The Barth–Nieto quintic is the closure of the set of points (x0:x1:x2:x3:x4:x5) of P5 satisfying the equations
The Barth–Nieto quintic is not rational, but has a smooth model that is a Calabi-Yau manifold
Calabi-Yau manifold
A Calabi-Yau manifold is a special type of manifold that shows up in certain branches of mathematics such as algebraic geometry, as well as in theoretical physics...
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