Tagged Questions

4
votes
1answer
85 views

Pullback of very ample sheaf again very ample? And other questions.

Let $S \subseteq \mathbb{P}^n$ be a smooth projective surface with given embedding in projective space. Moreover, let $X$ be another smooth surface and let there be a map $\pi: X \rightarrow S$ that ...
1
vote
1answer
124 views

(Continued:) finiteness of étale morphisms

I was writing a question, it became too long, and i decided to split it into two parts. I hope posting two questions at the same time is not a problem. First question: Checking flat- and smoothness: ...
1
vote
1answer
61 views

Checking flat- and smoothness: enough to check on closed points?

I am currently studying varieties over $\mathbb{C}$, i know some scheme theory. Let $f: X \rightarrow Y$ be a morphism of varieties. If we want to show flatness, is it enough to check the condition ...
7
votes
2answers
150 views

Fibres in algebraic geometry: multiplicity

Currently I am studying varieties over $\mathbb{C}$ and I know some scheme theory. My professor mentioned the other day that given a morphism of varieties over an alg. closed field $k$: $f: X ...