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Let $G$ be a finite subgroup of the group of automorphsims of a $K3$ surface $S$. Consider the quotient $S/G$.

I am interested in the collection of such qutients:

$$\{ S/G \mid S\text{ is a K3 surface, }G\text{ is a finite subgroup of }Aut(S) \}$$

Is there any classification result for the collection of quotients?

What if I assume that $G$ contains an involution that acts on $H^{2,0}(S)$ as multiplication by $-1$. Is the collection finite up to deformation?

Let $G$ be a finite subgroup of the group of automorphsims of a $K3$ surface $S$. Consider the quotient $S/G$.

I am interested in the collection of such qutients:

$$\{ S/G \mid S\text{ is a K3 surface, }G\text{ is a finite subgroup of }Aut(S) \}$$

Is there any classification result for the collection of quotients?

What if I assume that $G$ contains an involution that acts on $H^{2,0}(S)$ as multiplication by $-1$? Is the collection finite up to deformation?

Let $G$ be a finite subgroup of the group of automorphsims of a $K3$ surface $S$. I am considering the quotient $S/G$. Is there any classification result for the quotients?

What if I assume that $G$ contains an involution that acts on $H^{2,0}(S)$ as multiplication by $-1$. Are there only finitely many such quotients up to deformation?

Let $G$ be a finite subgroup of the group of automorphsims of a $K3$ surface $S$. Consider the quotient $S/G$.

I am interested in the collection of such qutients:

$$\{ S/G \mid S\text{ is a K3 surface, }G\text{ is a finite subgroup of }Aut(S) \}$$

Is there any classification result for the collection of quotients?

What if I assume that $G$ contains an involution that acts on $H^{2,0}(S)$ as multiplication by $-1$. Is the collection finite up to deformation?