algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, a Châtelet surface is a

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. Rational surfaces are the simplest of the 10 or so classes of su ...

studied by given by an equation :

y^2-az^2=P(x), \,

where ''P'' has degree 3 or 4. They are

conic bundle In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution of a Cartesian equation of the form : X^2 + aXY + b Y^2 = P (T).\, Theoretically, it can be considered as a Severi–Brauer surface, or more precisely as ...

References

* * {{DEFAULTSORT:Chatelet Surface Algebraic surfaces Complex surfaces