# 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.

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### Is every normalization a blowup?

Is the normalization of a variety always a blowup along some coherent ideal sheaf? If not, I would like to see a concrete counter-example. Let $Y \to X$ be the normalization. The answer is positive in ...
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### Cones of divisors on $\text{CDiv}(X)_{\mathbb{R}}$

Let $X$ be a normal, projective $\mathbb{Q}$-factorial variety over the complex numbers. I know that, in order to understand the birational geometry of $X$, one may consider several cones of divisors, ...
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### $A_1$ Du Val singularity and blow ups

Blowing up $\operatorname{Spec}K[x,y]=\mathbb{A}^2$ along $\operatorname{Spec}K[x,y]/(x^2,y)$ in the $U_B$ chart gives a singular point $U_B=\text{Spec}K[x,y][a]/(ya-x^2)$ at the origin. This ...
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### Blowup of diagonal in $\mathbb{P}^r \times \mathbb{P}^r$

Let $X= \mathbb{P}^r \times \mathbb{P}^r$. Suppose we blowup $X$ along $\Delta$ the diagonal to get $\tilde X$. I want to show that this is isomorphic to the fibre product which I describe below - Let ...
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### Connection between Chern classes and Blow ups

I know that a very important topological invariant in Complex Geometry and Algebraic Geometry is the Chern class of a vector bundle. Recently, I came across a paper discussing a potential connection ...
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### bigness of divisors under blow-up of finitely many points of the plane

Let $S\subset\mathbb{P}^2$ be a finite set of points in the plane, consider the blow-up of $\mathbb{P}^2$ along $S$: $$X=Bl_S(\mathbb{P^2})\rightarrow\mathbb{P}^2$$ and denote the divisor $D=2H-E$, ...
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### Study of the properties of a non-local ODE

I am studying the following non-local ODE $$\dot p(x) \nu_{\varepsilon, \alpha}(x) + \int_{x}^{2x_0}\frac{\dot p(s)}{s + \varepsilon} ds = c \quad \text{for } x \in [0,2x_0].$$ The number $x_0$ can ...
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