麻豆官网

As complex analytic surface, K3 is a deformation of a quartic surface in the projective 3-space. Only three finite (non-cyclic) simple groups, alternating A5, A6 and Klein鈥檚 L2(7), can act on a K3 surface bi-holomorphically. I consider the following three situations in which bigger ones can act:

• higher dimensional holomorphic symplectic manifolds of type K3[n] and OG10,
• K3 surfaces over a field of positive characteristic p > 0, especially supersingular ones, and
• symplectic manifolds in positive characteristic p > 0.

Three sporadic groups Higman-Sims (HS), McLaughlin (McL) and the third Conway group (Co3) are expected to have a birational action in the last case.