Rationality of the moduli spaces of Eisenstein 𝐾3 surfaces

Ma, Shouhei; Ohashi, Hisanori; Taki, Shingo

doi:10.1090/tran/6349

Rationality of the moduli spaces of Eisenstein $K3$ surfaces
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Trans. Amer. Math. Soc. 367 (2015), 8643-8679 Request permission

Abstract:

$K3$ surfaces with non-symplectic symmetry of order $3$ are classified by open sets of twenty-four complex ball quotients associated to Eisenstein lattices. We show that twenty-two of those moduli spaces are rational.

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