Barth–Nieto quintic

In algebraic geometry, the Barth–Nieto quintic is a quintic 3-fold in 4 (or sometimes 5) dimensional projective space studied by Wolf Barth and Isidro Nieto (1994) 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

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]

gollark: I mean, what are they meant to do, sell it with "4 cores", one of which doesn't work, or throw away the slightly broken ones?
gollark: Intel and AMD and probably all or almost of the ARM manufacturers do that though.
gollark: I don't see how that's a problem. You shouldn't really expect to get an extra working core if it's disabled.
gollark: Broken components? Isn't that talking about it being possible to enable extra cores?
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References
  1. Hulek, Klaus; Sankaran, Gregory K. (2002). "The geometry of Siegel modular varieties". Higher dimensional birational geometry (Kyoto, 1997). Advanced Studies in Pure Mathematics. 35. Tokyo: Math. Soc. Japan. pp. 89–156. doi:10.2969/aspm/03510089. MR 1929793.
  • Barth, Wolf; Nieto, Isidro (1994), "Abelian surfaces of type (1,3) and quartic surfaces with 16 skew lines", Journal of Algebraic Geometry, 3 (2): 173–222, ISSN 1056-3911, MR 1257320


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