Skip to main content
MathOverflow

Return to Question

Minor math Jaxing
Source Link
Daniele Tampieri
Daniele Tampieri
  • 6.4k
  • 7
  • 30
  • 45

Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that $X$ is normal and $Y$ is smooth. Let us write the largest open subset U of X such that $f^{-1}$ can be defined.

I want to show that $codim(X\backslash U)\geq2$$\operatorname{codim}(X\backslash U)\geq2$.

I think that I should use Zariski's main theorem but I don't know how to use. Thank you.

Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that $X$ is normal and $Y$ is smooth. Let us write the largest open subset U of X such that $f^{-1}$ can be defined.

I want to show that $codim(X\backslash U)\geq2$.

I think that I should use Zariski's main theorem but I don't know how to use. Thank you.

Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that $X$ is normal and $Y$ is smooth. Let us write the largest open subset U of X such that $f^{-1}$ can be defined.

I want to show that $\operatorname{codim}(X\backslash U)\geq2$.

I think that I should use Zariski's main theorem but I don't know how to use. Thank you.

added 20 characters in body
Source Link
Irish
Irish
  • 11
  • 2

Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that Y$X$ is normal and $Y$ is smooth. Let us write the largest open subset U of X such that $f^{-1}$ can be defined.

I want to show that $codim(X\backslash U)\geq2$.

I think that I should use Zariski's main theorem but I don't know how to use. Thank you.

Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that Y is normal. Let us write the largest open subset U of X such that $f^{-1}$ can be defined.

I want to show that $codim(X\backslash U)\geq2$.

I think that I should use Zariski's main theorem but I don't know how to use. Thank you.

Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that $X$ is normal and $Y$ is smooth. Let us write the largest open subset U of X such that $f^{-1}$ can be defined.

I want to show that $codim(X\backslash U)\geq2$.

I think that I should use Zariski's main theorem but I don't know how to use. Thank you.

Source Link
Irish
Irish
  • 11
  • 2

Exceptional locus of proper birational morphism from smooth variety to normal variety

Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that Y is normal. Let us write the largest open subset U of X such that $f^{-1}$ can be defined.

I want to show that $codim(X\backslash U)\geq2$.

I think that I should use Zariski's main theorem but I don't know how to use. Thank you.