\(K3\) surfaces with involution and analytic torsion. (English. Japanese original) Zbl 1446.32001
Sugaku Expo. 33, No. 1, 85-109 (2020); translation from Sūgaku 68, No. 3, 225-245 (2016).
Summary: In this article, recent progress of the holomorphic torsion invariant \(\tau_M\) of \(K3\) surfaces with involution is surveyed with a focus on its explicit expression as an automorphic function on the moduli space. A trinity of the Borcherds \(\Phi \)-function is also discussed as an important example.
MSC:
| 32-02 | Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces |
| 14-02 | Research exposition (monographs, survey articles) pertaining to algebraic geometry |
| 32J15 | Compact complex surfaces |
| 32N15 | Automorphic functions in symmetric domains |
| 14J28 | \(K3\) surfaces and Enriques surfaces |
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