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Let $X$ be a smooth projective variety of dimension $\geq 2$ and $E$ a vector bundle on $X$ of rank $r\geq 2$. Is it true that, if $E$ is globally generated, then the zero locus of a general section of $E$ has codimension $r$$\geq r$ in $X$?
Let $X$ be a smooth projective variety of dimension $\geq 2$ and $E$ a vector bundle on $X$ of rank $r\geq 2$. Is it true that, if $E$ is globally generated, then the zero locus of a general section of $E$ has codimension $r$ in $X$?
Let $X$ be a smooth projective variety of dimension $\geq 2$ and $E$ a vector bundle on $X$ of rank $r\geq 2$. Is it true that, if $E$ is globally generated, then the zero locus of a general section of $E$ has codimension $\geq r$ in $X$?
Let $X$ be a smooth projective variety of dimension $r\geq 2$$\geq 2$ and $E$ a vector bundle on $X$ of rank $\geq 2$$r\geq 2$. Is it true that, if $E$ is globally generated, then the zero locus of a general section of $E$ has codimension $r$ in $X$?
Let $X$ be a smooth projective variety of dimension $r\geq 2$ and $E$ a vector bundle on $X$ of rank $\geq 2$. Is it true that, if $E$ is globally generated, then the zero locus of a general section of $E$ has codimension $r$ in $X$?
Let $X$ be a smooth projective variety of dimension $\geq 2$ and $E$ a vector bundle on $X$ of rank $r\geq 2$. Is it true that, if $E$ is globally generated, then the zero locus of a general section of $E$ has codimension $r$ in $X$?
Vanishing locus of a general section of a vector bundle.
Let $X$ be a smooth projective variety of dimension $r\geq 2$ and $E$ a vector bundle on $X$ of rank $\geq 2$. Is it true that, if $E$ is globally generated, then the zero locus of a general section of $E$ has codimension $r$ in $X$?
