In algebraic geometry, the Barth-Nieto quintic is a quintic 3-fold in 4 (or sometimes 5) dimensional projective space studied by Barth & Nieto (1994) that is the Hessian of the Segre cubic. The Barth-Nieto quintic is the closure of the set of points 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.

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dbpprop:abstract
  • In algebraic geometry, the Barth-Nieto quintic is a quintic 3-fold in 4 (or sometimes 5) dimensional projective space studied by Barth & Nieto (1994) that is the Hessian of the Segre cubic. The Barth-Nieto quintic is the closure of the set of points 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> The Barth-Nieto quintic is not rational, but has a smooth model that is a Calabi-Yau manifold.
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  • Barth
  • Nieto
  • 1994 (xsd:integer)
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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 Barth & Nieto (1994) that is the Hessian of the Segre cubic. The Barth-Nieto quintic is the closure of the set of points 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.
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  • Barth–Nieto quintic
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