Skip to main content
MathOverflow

Return to Question

Fixed title
Source Link
gmvh
gmvh
  • 3.1k
  • 6
  • 27
  • 45

Blow-up of a three dimensional varitety-dimensional variety at a node

Let $X$ be a three dimensional-dimensional variety over $\mathbb{C}$ with a nodal singularity at a point, say $P$. Is the exceptional divisor of the blow-up of $X$ at $P$ isomorphic to a smooth quadric in $\mathbb{P}^3$? I read this statement in an article, but am not able to find a proof.

Blow-up of a three dimensional varitety at a node

Let $X$ be a three dimensional variety over $\mathbb{C}$ with a nodal singularity at a point, say $P$. Is the exceptional divisor of the blow-up of $X$ at $P$ isomorphic to a smooth quadric in $\mathbb{P}^3$? I read this statement in an article but not able to find a proof.

Blow-up of a three-dimensional variety at a node

Let $X$ be a three-dimensional variety over $\mathbb{C}$ with a nodal singularity at a point, say $P$. Is the exceptional divisor of the blow-up of $X$ at $P$ isomorphic to a smooth quadric in $\mathbb{P}^3$? I read this statement in an article, but am not able to find a proof.

Source Link
Jana
Jana
  • 2k
  • 12
  • 17

Blow-up of a three dimensional varitety at a node

Let $X$ be a three dimensional variety over $\mathbb{C}$ with a nodal singularity at a point, say $P$. Is the exceptional divisor of the blow-up of $X$ at $P$ isomorphic to a smooth quadric in $\mathbb{P}^3$? I read this statement in an article but not able to find a proof.