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Rationality of the moduli spaces of Eisenstein $ K3$ surfaces


Authors: Shouhei Ma, Hisanori Ohashi and Shingo Taki
Journal: Trans. Amer. Math. Soc. 367 (2015), 8643-8679
MSC (2010): Primary 14J28; Secondary 14G35, 14J26, 14E08
DOI: https://doi.org/10.1090/tran/6349
Published electronically: April 3, 2015
MathSciNet review: 3403068
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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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Additional Information

Shouhei Ma
Affiliation: Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan
Email: ma@math.nagoya-u.ac.jp, ma@math.titech.ac.jp

Hisanori Ohashi
Affiliation: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba, 278-8510, Japan
Email: ohashi@ma.noda.tus.ac.jp

Shingo Taki
Affiliation: School of Information Environment, Tokyo Denki University, 2-1200 Muzai Gakuendai, Inzai-shi, Chiba 270-1382, Japan
Email: staki@mail.dendai.ac.jp

DOI: https://doi.org/10.1090/tran/6349
Keywords: K3 surface, non-symplectic automorphism of order 3, moduli space, rationality, Eisenstein lattice, ball quotient
Received by editor(s): December 7, 2012
Received by editor(s) in revised form: October 18, 2013
Published electronically: April 3, 2015
Additional Notes: The first author was supported by Grant-in-Aid for JSPS fellows [21-978] and Grant-in-Aid for Scientific Research (S), No 22224001.
The second author was supported by Grant-in-Aid for Scientific Research (S), No 22224001 and for Young Scientists (B) 23740010.
Article copyright: © Copyright 2015 American Mathematical Society