The study of geometric objects defined by polynomial equations, as well as their generalizations: algebraic curves, such as elliptic curves, and more generally algebraic varieties, schemes, etc. Problems under this tag typically involve techniques of abstract algebra or complex-analytic methods. ...

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3
votes
0answers
32 views
+50

When will the support of a non-effective Cartier divisor be pure of codimension 1?

Let $X$ be a scheme and $D \in Div(X)$ a non-effective Cartier divisor. I am curious as to when $\text{Supp } D$ is pure of codimension 1, i.e all irreducible components are of codimension 1. So, ...
0
votes
0answers
38 views
+100

Number of fibrations over a curve.

Fix a non-singular complex projective curve $C$. I would like to know how many non-singular complex projective surfaces $S$ have the following properties (up to isomorphism): There is a fibration ...
5
votes
0answers
85 views
+100

Global generation of $\mathcal{O}_{\mathbb{P}(\mathcal{E})}(1)$ and $\mathcal{E}$

I'm trying to prove that $\mathcal{O}_{\mathbb{P}(\mathcal{E})}(1)$ is generated by global sections on $\mathbb{P}(\mathcal{E})$ if and only if $\mathcal{E}$ is generated by global sections ($\pi: ...