Assume that a finite group $G$ acts on a quasi-projective variety $Q$ (say, over complex numbers) that possesses a Zariski cover by $\le n$ affine varieties. My question is: does the quotient $Q/G$ admits a cover by $\le n$ affine varieties also? This fact seems to be well-known in the case $n=1$; certainly, in the general case the problem is to deal with non-$G$-stable covers.
$\begingroup$
$\endgroup$
asked Oct 12, 2015 at 7:00
Add a comment
|