Theta functions on the bounded symmetric domain of type \(I_{2,2}\) and the period map of a 4-parameter family of K3 surfaces. (English) Zbl 0791.32008
The inverse of the period map of the 4-dimensional family of K3 surfaces, the double covers of \(\mathbb{P}^ 2\) branching along six lines, is expressed by theta functions on the symmetric domain of type \(I_{2,2}\).
Reviewer: K.Matsumoto
MSC:
| 32G20 | Period matrices, variation of Hodge structure; degenerations |
| 14K25 | Theta functions and abelian varieties |
| 32N15 | Automorphic functions in symmetric domains |
| 32M15 | Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) |
| 14J10 | Families, moduli, classification: algebraic theory |
References:
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| [7] | [MSY1] Matsumoto, K., Sasaki, T., Yoshida, M.: The period of a 4-parameter family of K3 surfaces and the Aomoto-Gel’fand hypergeometric function of type (3, 6). Proc. Japan Acad, Ser. A64, 307-310 (1988) · Zbl 0684.14010 · doi:10.3792/pjaa.64.307 |
| [8] | [MSY2] Matsumoto, K., Sasaki, T., Yoshida, M.: The monodromy of the period map of a 4-parameter family of K3 surfaces and the hypergeometric function of type (3, 6). Int. J. Math.3, 1-164 (1992) · Zbl 0763.32016 · doi:10.1142/S0129167X92000023 |
| [9] | [Mu] Mumford, D.: Tata lectures on theta I, II. Boston: Birkh?user 1983, 1984 |
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