3
$\begingroup$

What is an example of an affine algebraic variety which is smooth but fails to be a complete intersection.

The standard example in projective space is the twisted cubic. So I thought of taking the affine cone of this, except that it fails to be smooth at the origin.

  • 0
    Can you intersect the cubic with the affine plane ? – 2017-01-10
  • 0
    No because you can move the residual line of intersection to infinity. – 2017-01-10
  • 1
    Some answers here: http://mathoverflow.net/questions/27197/local-complete-intersections-which-are-not-complete-intersections. – 2017-01-10

0 Answers 0