Is the canonical morphism $\mathbb A^n \to\mathbb A^{n-1}$ a projective morphism? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-21T10:01:13Z http://mathoverflow.net/feeds/question/112720 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/112720/is-the-canonical-morphism-mathbb-an-to-mathbb-an-1-a-projective-morphism Is the canonical morphism $\mathbb A^n \to\mathbb A^{n-1}$ a projective morphism? kwkwkw 2012-11-17T21:36:44Z 2012-11-18T11:55:13Z <p>Let $\mathbb A^n$ be the n-dimensional affine space over a field K (algebraically closed if that makes it easier), so $\mathbb A^n= \text{Spec }K[x_1,...,x_n]$, and $\mathbb A^{n-1}$ the (n-1)-dimensional analog. The inclusion $K[x_1,...,x_{n-1}]\to K[x_1,...,x_n]$ induces a map $\mathbb A^n \to\mathbb A^{n-1}$. Is this a projective map? </p>