# Questions tagged [blowup]

A technique in geometry (especially algebraic and differential, and, by extension, the study of pseudo-differential operators) for resolution of singularities. Not to be confused with the formation of singularities in solutions of ordinary or partial differential equations.

298 questions
Filter by
Sorted by
Tagged with
1 vote
70 views

18 views

### Doubt about the multiplicity of a point along a curve that lives in a surface

Suppose to have the following surface $S$ in $\mathbb{P}^3(x_0,x_1,x_2,x_3)$: $$x_3^6=x_0^6+x_1^6$$ Now consider the divisor $D:=(x_3)$ on $S$ and the point $p:=(1:e^{\frac{\pi i }{6}}:0:0)$ . Which ...
• 7,603
81 views

74 views

### How to show $x_0^2+x_1^2+x_2^2=0 \subset \mathbb{CP}^2 \iff \mathbb{CP}^1$

I am currently trying to blow-up an $A_n$ singularity defined by the hypersurface equation: \begin{equation} z_1^2+z_2^2+z_3^{n+1}=0 \subset \mathbb{C}^3 \end{equation} Let $x_i, i=0,1,2$ denote the ...
• 23
1 vote
22 views

• 831
1 vote
109 views

• 423
75 views

### Where do toric varieties appear naturally?

I'm reading Fulton's book. There's an awesome theorem that classifies all smooth toric surfaces as blowups at points starting from either $P^2$ or some Hirzebruch surface. I want to be more excited ...
• 1,824
1 vote
247 views

### Resolution of singularities of analytic spaces

It seems to me that the following resolution of singularities theorem (or a modification) is known to specialists but I have trouble finding references. Let $X$ be a complex analytic space, then there ...
• 336
44 views

### Minimal embedding for blowing ups

Let us consider the following specific problem for blowing-ups. Let $n$ be a large positive integer. Let $X\subset \mathbb P^n$ be a smooth sub variety of codimension $>1$. Denote $Y$ the blowing-...
• 336