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: They should really not be allowed to call it fibre.
gollark: Um, surely the other end kind of has to know that...?
gollark: To start, maybe just get a bunch of GPUs together on one system?
gollark: I think most homelab stuff ends up mostly running at 1% CPU most of the time.
gollark: https://tools.ietf.org/html/rfc3514 ← best RFC
References
- 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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