JournalsjemsVol. 11, No. 4pp. 799–818

K3 surfaces with a symplectic automorphism of order 11

  • Igor V. Dolgachev

    University of Michigan, Ann Arbor, United States
  • JongHae Keum

    Korea Institute for Advanced Study (KIAS), Seoul, South Korea
K3 surfaces with a symplectic automorphism of order 11 cover
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Abstract

We classify possible finite groups of symplectic automorphisms of K3 surfaces of order divisible by 11. The characteristic of the ground field must be equal to 11. The complete list of such groups consists of five groups: the cyclic group C11 of order 11, C11C5 , PSL2(F11) and the Mathieu groups _M_11, _M_22. We also show that a surface X admitting an automorphism g of order 11 admits a g-invariant elliptic fibration with the Jacobian fibration isomorphic to one of explicitly given elliptic K3 surfaces.

Cite this article

Igor V. Dolgachev, JongHae Keum, K3 surfaces with a symplectic automorphism of order 11. J. Eur. Math. Soc. 11 (2009), no. 4, pp. 799–818

DOI 10.4171/JEMS/167