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Multiple fibers on rational elliptic surfaces
Authors:
Brian Harbourne and William E. Lang
Journal:
Trans. Amer. Math. Soc. 307 (1988), 205-223
MSC:
Primary 14J27; Secondary 14J26
MathSciNet review:
936813
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Abstract: Our main result, Theorem (0.1), classifies multiple fibers on rational elliptic surfaces over algebraically closed fields of arbitrary characteristic. One result of this is the existence in positive characteristics of tame multiple fibers of additive type for several of the Kodaira fiber-types for which no examples were previously known.
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abéliennes sur les corps locaux et globaux, Inst. Hautes
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 surfaces over fields of characteristic two, Math. USSR Izv. 13 (1979), 147-165.
- 1.
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- [Do]
- I. Dolgachev, The Euler characteristic of a family of algebraic varieties, Math. USSR Sb. 18 (1972), 303-319. MR 0327774 (48:6116)
- [DR]
- P. Deligne and M. Rapoport, Las schemas de modules de courbes elliptiques, Antwerp Summer School, Springer Lecture Notes in Math., vol. 349, Springer-Verlag, Berlin and New York, 1973, pp. 143-316. MR 0337993 (49:2762)
- [Ga]
- R. Ganong, Kodaira dimension of embeddings of the line in the plane, J. Math. Kyoto Univ. 25 no. 4 (1985), 649-657. MR 810969 (87c:14013)
- [Ha]
- R. Hartshorne, Algebraic geometry, Graduate Texts in Math., no. 52, Springer-Verlag, Berlin and New York, 1977, p. 496. MR 0463157 (57:3116)
- [Ka]
- T. Katsura, On Kummer surfaces in characteristic
 , Proc. Internat. Sympos. on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Bookstore, Tokyo, 1978, pp. 525-542. MR 578870 (82d:14022)
- [Ko]
- K. Kodaira, On compact analytic surfaces. II, Ann. of Math. (2) 77 (1963), 563-626.
- [KU]
- T. Katsura and K. Ueno, Multiple singular fibers of type
 of elliptic surfaces in characteristic p, preprint, 1985. MR 799664 (87g:14040)
- [L1]
- W. E. Lang, Review of T. Katsura's paper On Kummer surfaces in characteristic (see above citation). MR 82d: 14022.
- [L2]
- -, Quasi-elliptic surfaces in characteristic
 , Ann. Sci. Éole Norm. Sup. (4) 12 (1979), 473-500. MR 565468 (83d:14021)
- [L3]
- -, On the Euler number of algebraic surfaces in characteristic , Amer. J. Math. 108 (1980), 511-516.
- [L4]
- -, An analogue of the logarithmic transform in characteristic , Proc. 1984 Vancouver Summer Conf. on Algebraic Geometry, Canad. Math. Soc. Conf. Proc., vol. 6, 1986, pp. 337-340.
- [M]
- Yu. Manin, Cubic forms: algebra, geometry, arithmetic, North-Holland, Amsterdam, 1974. MR 833513 (87d:11037)
- [Mi]
- J. S. Milne, Étale cohomology, Princeton Univ. Press, Princeton, N.J., 1980, xiii and 323. MR 559531 (81j:14002)
- [Mu]
- D. Mumford, Enriques classification of surfaces in
 . I, Global Analysis, Papers in Honor of K. Kodaira, 1969, pp. 325-339. MR 0254053 (40:7266)
- [N]
- A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Inst. Hautes Études. Sci. Publ. Math. 21 (1964). MR 0179172 (31:3423)
- [O]
- A. P. Ogg, Elliptic curves and wild ramification, Amer. J. Math. 89 (1967), 1-21. MR 0207694 (34:7509)
- [R]
- M. Raynaud, Specialisation du functeur de Picard, Inst. Hautes Études Sci. Publ. Math. 38 (1970), 27-76. MR 0282993 (44:227)
- [RS]
- A. N. Rudakov and I. R. Shafarevich, Supersingular surfaces over fields of characteristic two, Math. USSR Izv. 13 (1979), 147-165.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1988-0936813-6
PII:
S 0002-9947(1988)0936813-6
Keywords:
Rational,
elliptic,
surface,
multiple fiber,
positive characteristic
Article copyright:
© Copyright 1988 American Mathematical Society
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