**6**

votes

**2**answers

769 views

### Anticanonical divisor of the blow up of P^2 in 9 points

Let $S$ the blow up of $P^2$ in nine points. Why is the anticanonical divisor $-K_S$ not semiample?

**4**

votes

**1**answer

523 views

### A working generalization of Weil divisors

Hartshorne defines Weil divisors under the hypotheses "Noetherian integral separated scheme regular in codimension 1", which, for example, ensures that the divisor of a rational function is a finite ...

**5**

votes

**1**answer

274 views

### Is there a canonical notion of principal divisor on a discrete dynamical system?

I hope this question is well-posed.
Let (X, f) be a discrete dynamical system such that every x in X has finite period, i.e. there is some n such that f^n(x) = x. Let Div(X) be the free abelian ...

**8**

votes

**2**answers

2k views

### does a line bundle always have a degree

For curves there is a very simple notion of degree of a line bundle or equivalently of a Weil or Cartier divisor. Even in any projective space $\mathbb P(V)$ divisors are cut out by hypersurfaces ...

**5**

votes

**3**answers

382 views

### Weil divisors on non Noetherian schemes

Let X be an integral scheme that is separated (say over an affine scheme). Define a Weil divisor as a finite integral combination of height 1 points of X, where the height of a point of X is the ...