Bordiga surface
Encyclopedia
In algebraic geometry
, a Bordiga surface is a certain sort of rational surface
of degree 6 in P4.
A Bordiga surface is isomorphic to the projective plane blown up
in 10 points, the embedding into P4 is given by the 5-dimensional space of quartics passing through the 10 points. White surface
s are the generalizations using more points.
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, a Bordiga surface is a certain sort of rational surface
Rational surface
In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two...
of degree 6 in P4.
A Bordiga surface is isomorphic to the projective plane blown up
Blowing up
In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the point with the projectivized tangent space at that point...
in 10 points, the embedding into P4 is given by the 5-dimensional space of quartics passing through the 10 points. White surface
White surface
In algebraic geometry, a White surface is one of the rational surfaces in Pn studied by , generalizing cubic surfaces and Bordiga surfaces, which are the cases n = 3 or 4....
s are the generalizations using more points.