On the divisor of involutions in an elliptic modular surface
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- by P. R. Hewitt PDF
- Proc. Amer. Math. Soc. 110 (1990), 573-581 Request permission
Abstract:
Let $E \to X$ be an elliptic modular surface and $S$ the tangential ruled surface of a projective embedding of $X$. The divisor that collects the involutions of the elliptic fibers of $E$ is precisely the branch locus of $E \to S$ (at least generically). In this paper, we present two theorems that characterize this divisor in terms of the action of the group of modular automorphisms. These results extend work of D. Burns [1].References
- D. Burns, On the geometry of elliptic modular surfaces and representations of finite groups, Algebraic geometry (Ann Arbor, Mich., 1981) Lecture Notes in Math., vol. 1008, Springer, Berlin, 1983, pp. 1–29. MR 723705, DOI 10.1007/BFb0065696
- Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
- Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Kanô Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Publications of the Mathematical Society of Japan, No. 11. MR 0314766
- Tetsuji Shioda, On elliptic modular surfaces, J. Math. Soc. Japan 24 (1972), 20–59. MR 429918, DOI 10.2969/jmsj/02410020
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 573-581
- MSC: Primary 14J27; Secondary 11F99, 11G99, 14J50
- DOI: https://doi.org/10.1090/S0002-9939-1990-1028286-7
- MathSciNet review: 1028286