1
vote
0answers
89 views

Projective scheme

How can I prove that the two different construction of $\mathbb{P}_k^n$ (as $Proj K[x_0,x_1,...,x_n]$ and by gluing copies of $\mathbb{A}_k^n$) agree? And how can I prove that if $A$ is reduced also ...
4
votes
1answer
152 views

The canonical divisor of the projective line

Let $A$ be a ring. Assume it has some nice properties if necessary, e.g., $A$ is a Dedekind domain. Let $\mathbf{P}^1_A$ be the projective line over $A$. I want to show that $-2 [\infty]$ is a ...
3
votes
1answer
180 views

closed subschemes of projective space over a scheme

Let $X$ be an integral Noetherian scheme. If $Z \subset \mathbb{P}^n_{\mathbb{Z}}$ is a closed subscheme, under what conditions can we say that the codimension of $X \times Z \subset \mathbb{P}^n_X$ ...