List of complex and algebraic surfaces

This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification. == Kodaira dimension −∞ == === Rational surfaces === Projective plane ==== Quadric surfaces ==== Cone (geometry) Cylinder Ellipsoid Hyperboloid Paraboloid Sphere Spheroid ==== Rational cubic surfaces ==== Cayley nodal cubic surface, a certain cubic surface with 4 nodes Cayley's ruled cubic surface Clebsch surface or Klein icosahedral surface Fermat cubic Monkey saddle Parabolic conoid Plücker's conoid Whitney umbrella ==== Rational quartic surfaces ==== Châtelet surfaces Dupin cyclides, inversions of a cylinder, torus, or double cone in a sphere Gabriel's horn Right circular conoid Roman surface or Steiner surface, a realization of the real projective plane in real affine space Tori, surfaces of revolution generated by a circle about a coplanar axis ==== Other rational surfaces in space ==== Boy's surface, a sextic realization of the real projective plane in real affine space Enneper surface, a nonic minimal surface Henneberg surface, a minimal surface of degree 15 Bour's minimal surface, a surface of degree 16 Richmond surfaces, a family of minimal surfaces of variable degree ==== Other families of rational surfaces ==== Coble surfaces Del Pezzo surfaces, surfaces with an ample anticanonical divisor Hirzebruch surfaces, rational ruled surfaces Segre surfaces, intersections of two quadrics in projective 4-space Unirational surfaces of characteristic 0 Veronese surface, the Veronese embedding of the projective plane into projective 5-space White surfaces, the blow-up of the projective plane at n + 1 C 2 {\displaystyle _{n+1}C_{2}} points by the linear system of degree- n {\displaystyle n} curves through those points Bordiga surfaces, the White surfaces determined by families of quartic curves === Non-rational ruled surfaces === === Class VII surfaces === Vanishing second Betti number: Hopf surfaces Inoue surfaces; several other families discovered by Inoue have also been called "Inoue surfaces" Positive second Betti number: Enoki surfaces Inoue–Hirzebruch surfaces Kato surfaces == Kodaira dimension 0 == === K3 surfaces === Kummer surfaces Tetrahedroids, special Kummer surfaces Wave surface, a special tetrahedroid Plücker surfaces, birational to Kummer surfaces Weddle surfaces, birational to Kummer surfaces Smooth quartic surfaces Supersingular K3 surfaces === Enriques surfaces === Reye congruences, the locus of lines that lie on at least two quadrics in a general three dimensional linear system of quadric surfaces in projective 3-space P 3 {\displaystyle \mathbb {P} ^{3}} .

Source: Wikipedia — List of complex and algebraic surfaces (CC BY-SA 4.0)

List of complex and algebraic surfaces

This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification. == Kodaira dimension −∞ == === Rational surfaces === Projective plane ==== Quadric surfaces ==== Cone (geometry) Cylinder Ellipsoid Hyperboloid Paraboloid Sphere Spheroid ==== Rational cubic surfaces ==== Cayley nodal cubic surface, a certain cubic surface with 4 nodes Cayley's ruled cubic surface Clebsch surface or Klein icosahedral surface Fermat cubic Monkey saddle Parabolic conoid Plücker's conoid Whitney umbrella ==== Rational quartic surfaces ==== Châtelet surfaces Dupin cyclides, inversions of a cylinder, torus, or double cone in a sphere Gabriel's horn Right circular conoid Roman surface or Steiner surface, a realization of the real projective plane in real affine space Tori, surfaces of revolution generated by a circle about a coplanar axis ==== Other rational surfaces in space ==== Boy's surface, a sextic realization of the real projective plane in real affine space Enneper surface, a nonic minimal surface Henneberg surface, a minimal surface of degree 15 Bour's minimal surface, a surface of degree 16 Richmond surfaces, a family of minimal surfaces of variable degree ==== Other families of rational surfaces ==== Coble surfaces Del Pezzo surfaces, surfaces with an ample anticanonical divisor Hirzebruch surfaces, rational ruled surfaces Segre surfaces, intersections of two quadrics in projective 4-space Unirational surfaces of characteristic 0 Veronese surface, the Veronese embedding of the projective plane into projective 5-space White surfaces, the blow-up of the projective plane at n + 1 C 2 {\displaystyle _{n+1}C_{2}} points by the linear system of degree- n {\displaystyle n} curves through those points Bordiga surfaces, the White surfaces determined by families of quartic curves === Non-rational ruled surfaces === === Class VII surfaces === Vanishing second Betti number: Hopf surfaces Inoue surfaces; several other families discovered by Inoue have also been called "Inoue surfaces" Positive second Betti number: Enoki surfaces Inoue–Hirzebruch surfaces Kato surfaces == Kodaira dimension 0 == === K3 surfaces === Kummer surfaces Tetrahedroids, special Kummer surfaces Wave surface, a special tetrahedroid Plücker surfaces, birational to Kummer surfaces Weddle surfaces, birational to Kummer surfaces Smooth quartic surfaces Supersingular K3 surfaces === Enriques surfaces === Reye congruences, the locus of lines that lie on at least two quadrics in a general three dimensional linear system of quadric surfaces in projective 3-space P 3 {\displaystyle \mathbb {P} ^{3}} .

Source: Wikipedia "List of complex and algebraic surfaces" · CC BY-SA 4.0

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