# Tagged Questions

**3**

votes

**1**answer

145 views

### Blowing up rational singularities

Let $X$ be a projective surface embedded into $\mathbb{P}^n_{\mathbb{C}}$ having at most rational singularities. Let $\tilde{X} \to X$ be the minimal resolution of $X$. Is it possible to embed ...

**2**

votes

**3**answers

329 views

### Divisor class group on blowup of nodal surface

The following got no answer on mathstackexchange. I believe it not to be hard, but maybe it is a little specialized?
All varieties will be over $\mathbb{C}$ and projective unless stated otherwise.
...

**15**

votes

**2**answers

671 views

### When does the blow-up of $CP^2$ at N points embed in $CP^4$?

Write $X_N$ for this blow up. Place the N points in 'general position' as needed. Then $X_6$ embeds in $CP^2$ as a smooth cubic surface. (See, eg, Griffiths and Harris.) But there is no other ...

**2**

votes

**1**answer

340 views

### Resolution of “nice” and zero-dimensional singularities on a surface

Assume I have a singular algebraic surface $X$ over an algebraically closed field (characteristic zero if you want) which is singular in a finite set of points. I am looking for a condition as to the ...