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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$\begingroup$ This seems to answer (1): mathoverflow.net/questions/122922/group-actions-on-blow-ups/… $\endgroup$– Daniel LoughranCommented Dec 3, 2014 at 21:56
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$\begingroup$ yeah, the ideas in that reference also handles (2). $\endgroup$– ivainsencherCommented Dec 4, 2014 at 23:37
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