White surface
Encyclopedia
In algebraic geometry
, a White surface is one of the rational surface
s in Pn studied by , generalizing cubic surface
s and Bordiga surface
s, which are the cases n = 3 or 4.
A White surface in Pn is given by the embedding of P2 blown up
in n(n + 1)/2 points by the linear system of degree n curves through these 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 White surface is one of the 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...
s in Pn studied by , generalizing cubic surface
Cubic surface
A cubic surface is a projective variety studied in algebraic geometry. It is an algebraic surface in three-dimensional projective space defined by a single polynomial which is homogeneous of degree 3...
s and Bordiga surface
Bordiga surface
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 surfaces...
s, which are the cases n = 3 or 4.
A White surface in Pn is given by the embedding of P2 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 n(n + 1)/2 points by the linear system of degree n curves through these points.