Châtelet surface
Encyclopedia
In algebraic geometry
, a Châtelet surface is a rational surface
studied by given by an equation
where P has degree 3 or 4. They are conic bundle
s.
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 Châtelet surface is a 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...
studied by given by an equation
where P has degree 3 or 4. They are conic bundle
Conic bundle
In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution of a Cartesian equation of the formTheoretically, it can be considered as a Severi–Brauer surface, or more precisely as a Châtelet surface. This can be a double covering of a ruled surface...
s.