Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] D. Burns, On elliptic modular surfaces and representations of finite groups, Lecture Notes in Math., vol. 1008, Springer-Verlag, 1983, pp. 1-29. MR 723705 (86a:14037)
  • [2] R. Hartshorne, Algebraic geometry, Graduate Texts in Math., vol. 52, Springer-Verlag, New York, 1980. MR 0463157 (57:3116)
  • [3] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton University Press, Princeton, 1971. MR 0314766 (47:3318)
  • [4] T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan 24 (1972), 20-59. MR 0429918 (55:2927)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14J27, 11F99, 11G99, 14J50

Retrieve articles in all journals with MSC: 14J27, 11F99, 11G99, 14J50

Additional Information

Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society