# Tagged Questions

**1**

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**0**answers

69 views

### invariance of the dimension of severi varieties of surfaces

Suppose I have a smooth projective surface $S\subset P^n$ embedded by a very ample linear system $|L|$. Consider now the generalized Severi varieties that parametrize curves on $S$ belonging to $|L|$, ...

**9**

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**3**answers

725 views

### Extending birational isomorphisms between planar curves to the P^2

Let $k$ be a field and let $C,D$ be two integral curves in $\mathbb{P}^2_k$. Now let $f:C \to D$ be a birational isomorphism. Can $f$ be extended to $\mathbb{P}^2_k$. To be precise, does there exist a ...

**1**

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**1**answer

240 views

### 'Reference' request: Program to work with cyclic quotient singularities.

I'm looking for program code to deal with cyclic quotient singularities on normal surfaces. In particular, at the moment I need that given a singularity $p$ like $p=\frac{1}{n}(1,a)$ the code ...

**4**

votes

**1**answer

553 views

### Example of cone of numerically effective curves which is not polyhedral

I think I have seen more than one reference in which the cone of numerically effective curves can be 'not polyhedral', i.e. with an infinite number of extremal rays
I cannot remember where I read ...

**1**

vote

**2**answers

240 views

### Numerically negative exceptional divisor on a surface.

Suppose $S$ is an algebraic surface (possibly projective) over an algebraically closed field $k$. Suppose $D_i$ are irreducible smooth curves (rational, if you want) with negative self-intersection ...

**2**

votes

**2**answers

283 views

### Global sections of a linear system

Recently, following Beauville's book (exercises iv.(1),(2)) I have been working on Hirzebruch surfaces (from the algebraic geometry point of view) and I had to compute the space of global sections of ...