Английская Википедия:Barth–Nieto quintic
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In algebraic geometry, the Barth–Nieto quintic is a quintic 3-fold in 4 (or sometimes 5) dimensional projective space studied by Шаблон:Harvs that is the Hessian of the Segre cubic.
Definition
The Barth–Nieto quintic is the closure of the set of points (x0:x1:x2:x3:x4:x5) of P5 satisfying the equations
- <math>\displaystyle x_0+x_1+x_2+x_3+x_4+x_5= 0</math>
- <math>\displaystyle x_0^{-1}+x_1^{-1}+x_2^{-1}+x_3^{-1}+x_4^{-1}+x_5^{-1} = 0.</math>
Properties
The Barth–Nieto quintic is not rational, but has a smooth model that is a modular Calabi–Yau manifold with Kodaira dimension zero. Furthermore, it is birationally equivalent to a compactification of the Siegel modular variety A1,3(2).[1]
References
Шаблон:Algebraic-geometry-stub