page_title: Barth surface
hierarchical_section_title: Barth surface
caption_attribution_description: English: Barth Decic surface
context_page_description: 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. 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, David Jaffe and Daniel Ruberman 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.
context_section_description: 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,  David Jaffe and Daniel 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.
caption: Barth Decic
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