algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

, a Bordiga surface is a certain sort of

rational surface In algebraic geometry, a branch of mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sc ...

of degree 6 in ''P''⁴, introduced by

Giovanni Bordiga upright=1.1, Giovanni Bordiga by Lino Selvatico Giovanni Bordiga (2 April 1854 in Novara – 16 June 1933 in Venice) was an Italian mathematician who worked on algebraic and projective geometry at the university of Padua. He introduced the Bor ...

. A Bordiga surface is isomorphic to the projective plane blown up in 10 points, the embedding into ''P''⁴ is given by the 5-dimensional space of quartics passing through the 10 points.

White surface In algebraic geometry, a White surface is one of the rational surfaces in ''P'n'' studied by , generalizing cubic surfaces and Bordiga surfaces, which are the cases ''n'' = 3 or 4. A White surface in ''P'n'' is given by the embedding of ...

s are the generalizations using more points.

References

* Complex surfaces Algebraic surfaces {{algebraic-geometry-stub