On the divisor of involutions in an elliptic modular surface

Author:
P. R. Hewitt

Journal:
Proc. Amer. Math. Soc. **110** (1990), 573-581

MSC:
Primary 14J27; Secondary 11F99, 11G99, 14J50

MathSciNet review:
1028286

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Abstract: Let be an elliptic modular surface and the tangential ruled surface of a projective embedding of . The divisor that collects the involutions of the elliptic fibers of is precisely the branch locus of (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].

**[1]**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**, 10.1007/BFb0065696**[2]**Robin Hartshorne,*Algebraic geometry*, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR**0463157****[3]**Goro Shimura,*Introduction to the arithmetic theory of automorphic functions*, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Kan\cflex o Memorial Lectures, No. 1. MR**0314766****[4]**Tetsuji Shioda,*On elliptic modular surfaces*, J. Math. Soc. Japan**24**(1972), 20–59. MR**0429918**

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1028286-7

Article copyright:
© Copyright 1990
American Mathematical Society