Category: 3-folds

Cubic threefold
In algebraic geometry, a cubic threefold is a hypersurface of degree 3 in 4-dimensional projective space. Cubic threefolds are all unirational, but used intermediate Jacobians to show that non-singula
Quartic threefold
In algebraic geometry, a quartic threefold is a degree 4 hypersurface of dimension 3 in 4-dimensional projective space. showed that all non-singular quartic threefolds are irrational, though some of t
Quintic threefold
In mathematics, a quintic threefold is a 3-dimensional hypersurface of degree 5 in 4-dimensional projective space. Non-singular quintic threefolds are Calabi–Yau manifolds. The Hodge diamond of a non-
Minimal model program
In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Its goal is to construct a birational model of any complex projective variety which is
Koras–Russell cubic threefold
In algebraic geometry, the Koras–Russell cubic threefolds are smooth affine complex threefolds diffeomorphic to studied by . They have a hyperbolic action of a one-dimensional torus with a unique fixe
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 that is the Hessian of the Segre cubic.
Klein cubic threefold
In algebraic geometry, the Klein cubic threefold is the non-singular cubic threefold in 4-dimensional projective space given by the equation studied by .Its automorphism group is the group PSL2(11) of
Segre cubic
In algebraic geometry, the Segre cubic is a cubic threefold embedded in 4 (or sometimes 5) dimensional projective space, studied by Corrado Segre.
Line complex
In algebraic geometry, a line complex is a 3-fold given by the intersection of the Grassmannian G(2, 4) (embedded in projective space P5 by Plücker coordinates) with a hypersurface. It is called a lin
In algebraic geometry, a 3-fold or threefold is a 3-dimensional algebraic variety. The Mori program showed that 3-folds have minimal models.
Fano variety
In algebraic geometry, a Fano variety, introduced by Gino Fano in (Fano , ), is a complete variety X whose anticanonical bundle KX* is ample. In this definition, one could assume that X is smooth over
Consani–Scholten quintic
In the mathematical fields of algebraic geometry and arithmetic geometry, the Consani–Scholten quintic is an algebraic hypersurface (the set of solutions to a single polynomial equation in multiple va
Burkhardt quartic
In mathematics, the Burkhardt quartic is a quartic threefold in 4-dimensional projective space studied by Burkhardt , with the maximum possible number of 45 nodes.
Fermat quintic threefold
In mathematics, a Fermat quintic threefold is a special quintic threefold, in other words a degree 5, dimension 3 hypersurface in 4-dimensional complex projective space, given by the equation . This t
Igusa quartic
In algebraic geometry, the Igusa quartic (also called the Castelnuovo–Richmond quartic CR4 or the Castelnuovo–Richmond–Igusa quartic) is a quartic hypersurface in 4-dimensional projective space, studi