In algebraic geometry, a Barth surface is one of the complex nodal surfaces in 3 dimensions with large numbers of double points found by Wolf Barth (1996). Two examples are the Barth sextic of degree 6 with 65 double points, and the Barth decic of degree 10 with 345 double points.
Some admit icosahedral symmetry.
For degree 6 surfaces in P3, Jaffe & Ruberman (1997) showed that 65 is the maximum number of double points possible. The Barth sextic is a counterexample to an incorrect claim by Francesco Severi in 1946 that 52 is the maximum number of double points possible.
- Barth, W. (1996), "Two projective surfaces with many nodes, admitting the symmetries of the icosahedron", Journal of Algebraic Geometry 5 (1): 173–186, MR 1358040.
- Jaffe, David B.; Ruberman, Daniel (1997), "A sextic surface cannot have 66 nodes", Journal of Algebraic Geometry 6 (1): 151–168, MR 1486992.
- Barth sextic
- Barth decic
- Weisstein, Eric W., "Barth Sextic", MathWorld.
- Weisstein, Eric W., "Barth Decic", MathWorld.
- animations of Barth surfaces
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