# Tagged Questions

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**0**answers

111 views

### A question on resolution of singularities

I am wondering if it could be possible in particular cases to resolve a singularity of dimension $n$ by blowing-up a locus of dimension smaller than $n$.
For instance consider a cubic surface ...

**2**

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**1**answer

119 views

### Singularities of secant varieties of rational normal curves

Let $C\subset\mathbb{P}^n$ be a rational normal curve of degree $n$, and let $Sec_k(C)\subset\mathbb{P}^n$ be its $k$-th secant variety. By Theorem 1.1 in this paper:
...

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**1**answer

404 views

### Top self-intersection of exceptional divisors

Let $Y\subset\mathbb{P}^n$ be a smooth variety of codimension two. Consider the blow-up $X = Bl_Y\mathbb{P}^n$ of $\mathbb{P}^n$ along $Y$, and let $E$ be the exceptional divisor over $Y$. Then $E$ ...

**1**

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**1**answer

220 views

### blow-up along singular variety

Can somebody give me a nice example of blow-up of a smooth algebraic variety along a singular subvariety? Something I can do some exercise on and check the differences with a smooth blow-up. Thanks!

**2**

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**2**answers

388 views

### Components of an exceptional divisor

Let $X$ be a projective variety and let $\tilde{X}$ be the blow-up of $X$ at a subscheme $Z$. Let $F$ be the exceptional divisor of $\tilde{X}$. I wonder:
What is the number of irreducible ...