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Alex Degtyarev
Alex Degtyarev
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Let X$X$,Y $Y$ be a smooth projective varieties, say over the complex numbers, both acted upon by a connected linear group G$G$. Let f:X-->Y$f\colon X\to Y$ be an equivariant rational map. Let Z$Z$ be a smooth G$G$-subvariety sitting in the indeterminacy locus of f$f$. Let X'$X'$ be the blowup of Z$Z$ in X$X$. Wish a reference to show (1) the action of G$G$ extends to X'$X'$, and (2) the rational map f:X'-->Y$f\colon X'\to Y$ induced by f$f$ is equivariant.

Let X,Y be a smooth projective varieties, say over the complex numbers, both acted upon by a connected linear group G. Let f:X-->Y be an equivariant rational map. Let Z be a smooth G-subvariety sitting in the indeterminacy locus of f. Let X' be the blowup of Z in X. Wish a reference to show (1) the action of G extends to X', and (2) the rational map f:X'-->Y induced by f is equivariant.

Let $X$, $Y$ be a smooth projective varieties, say over the complex numbers, both acted upon by a connected linear group $G$. Let $f\colon X\to Y$ be an equivariant rational map. Let $Z$ be a smooth $G$-subvariety sitting in the indeterminacy locus of $f$. Let $X'$ be the blowup of $Z$ in $X$. Wish a reference to show (1) the action of $G$ extends to $X'$, and (2) the rational map $f\colon X'\to Y$ induced by $f$ is equivariant.

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ivainsencher
ivainsencher
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inducing group action on a blowup

Let X,Y be a smooth projective varieties, say over the complex numbers, both acted upon by a connected linear group G. Let f:X-->Y be an equivariant rational map. Let Z be a smooth G-subvariety sitting in the indeterminacy locus of f. Let X' be the blowup of Z in X. Wish a reference to show (1) the action of G extends to X', and (2) the rational map f:X'-->Y induced by f is equivariant.