Galois covers between $K3$ surfaces

Abstract

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Finite symplectic actions on the K3 lattice

“…After a result of Nikulin [20], Mukai [18] classified finite groups which act on K3 surfaces faithfully and symplectically by listing the 11 maximal groups (see Theorem 2.4). Xiao [29] gave another proof of Mukai's result by studying the singularities of the quotient G\X for a K3 surface X with a symplectic action of a finite group G. Moreover, he showed the following.…”

“…In this paper, we prove that the above uniqueness holds for any finite groups except for five groups (see Theorem 8.10). We use the same notation for groups as in [29] (see Table 10.2).…”

Classification of extremal elliptic K3 surfaces and fundamental groups of open K3 surfaces

“…Mukai [9] presented the complete list of symplectic automorphism groups of K3 surfaces. (See also Kondō [6] and Xiao [18].) Under Hypothesis, therefore, we know what groups can appear as π 1 (X \ ∆).…”

Galois Coverings of the Plane by K3 Surfaces

“…which is isomorphic to (Z/(2)) 4 and is of order 16. In order to show that F 1 is uniformizable, one must verify that the subgroups κ and λ i are isomorphic to Z/(2) and the subgroups κ, λ j and λ i , λ j are isomorphic to Z/(2) ⊕ Z/(2) for any i = j ∈ [1,4].…”