Lesson plan
conic bundle
In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution to a Cartesian equation of the form: : X^2 + aXY + b Y^2 = P (T).\, Conic bundles can be considered as either a Severi–Brauer or Châtelet surface. This can be a double covering of a ruled surface. It can be associated with the symbol (a, P) in the second Galois cohomology of the field k through an isomorphism. In practice, it is more commonly observed as a surface with a well-understood divisor class group, and the simplest cases share with Del Pezzo surfaces the property of being a rational surface. But many problems of contemporary mathematics remain open, notably, for those examples which are not rational, the question of unirationality.
Article summary
In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution to a Cartesian equation of the form: : X^2 + aXY + b Y^2 = P (T).\, Conic bundles can be considered as either a Severi–Brauer or Châtelet surface. This can be a double covering of a ruled surface. It can be associated with the symbol (a, P) in the second Galois cohomology of the field k through an isomorphism. In practice, it is more commonly observed as a surface with a well-understood divisor class group, and the simplest cases share with Del Pezzo surfaces the property of being a rational surface. But many problems of contemporary mathematics remain open, notably, for those examples which are not rational, the question of unirationality.
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