代数几何Prove that the variety P²\X,where X is a plane conic,is affine.[Hint:Use the Veronese embedding.]

代数几何Prove that the variety P²\X,where X is a plane conic,is affine.[Hint:Use the Veronese embedding.]
代数几何
Prove that the variety P²\X,where X is a plane conic,is affine.[Hint:Use the Veronese embedding.]

代数几何Prove that the variety P²\X,where X is a plane conic,is affine.[Hint:Use the Veronese embedding.]
提示已经比较充分了.
在嵌入P² → P⁵,(X:Y:Z) → (X²:Y²:Z²:XY:YZ:ZX)下,P²被嵌入为P⁵中的一个射影曲面S.
同时X = V(aX²+bY²+cZ²+dXY+eYZ+fZX)被嵌入超平面H = V(aX+bY+cZ+dW+eU+fV).
于是P²\X同构于S\H,后者是P⁵\H ≌ A⁵中的一个仿射曲面.