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Book Review

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Book Information:

Author: M. Miyanishi
Title: Curves on rational and unirational surfaces
Additional book information: Tata Institute of Fundamental Research, Bombay, 1978, Narosa Publishing House, New Delhi, 1978, 307 pp., $9.90.

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

  • 1. S. S. Abhyankar, Algebraic space curves, Séminaire de Mathématiques Supérieures, Université de Montréal, 1970. MR 399109
  • 2. S. S. Abhyankar, P. Eakin and W. Heinzer, On the uniqueness of the ring of coefficients in a polynomial ring, J. Algebra 23 (1972), 310-342. MR 306173
  • 3. S. S. Abhyankar and T. T. Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1976), 148-166. MR 379502
  • 4. S. S. Abhyankar, Lectures on expansion techniques in algebraic geometry, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 57, Tata Institute of Fundamental Research, Bombay, 1977. Notes by Balwant Singh. MR 542446
  • 5. E. Bombieri and D. Husemoller, Classification and embeddings of surfaces, Algebraic Geometry-Arcata 1974, Proc. Sympos. Pure Math., vol. 29, Amer. Math. Soc., Providence, R. I., 1975, pp. 329-420. MR 506292
  • 6. P. Eakin and W. Heinzer, A cancellation problem for rings, Conference on Commutative Algebra (Univ. Kansas, Lawrence, Kansas, 1972), Lecture Notes in Math., vol. 311, Springer, Berlin, 1973, pp. 61-77. MR 349664
  • 7. D. Eisenbud and E. G. Evans, Jr., Every algebraic set in n-space is the intersection of n hypersurfaces, Invent. Math. 19 (1973), 107-112. MR 327783
  • 8. Takao Fujita, On Zariski problem, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), no. 3, 106–110. MR 531454
  • 9. Richard Ganong, On plane curves with one place at infinity, J. Reine Angew. Math. 307/308 (1979), 173–193. MR 534219, https://doi.org/10.1515/crll.1979.307-308.173
  • 10. A. Grothendieck, Eléments de Géométrie Algébrique, Publ. Math. Inst. Hautes Étude Sci., 1960-1967.
  • 11. M. Hochster, Nonuniqueness of coefficient rings in a polynomial ring, Proc. Amer. Math. Soc. 34 (1972), 81-82. MR 294325
  • 12. S. Iitaka, On logarithmic Kodaira dimension of algebraic varieties, Complex Analysis and Algebraic Geometry, Tokyo, Iwanami Shoten, Cambridge University Press, London and New York, 1977. MR 569688
  • 13. S. Iitaka, Logarithmic forms on algebraic varieties, J. Fac. Sci. Univ. Tokyo (Sec. 1A), 23 (1976), 525-544. MR 429884
  • 14. T. Kambayashi, M. Miyanishi and M. Takeuchi, Unipotent algebraic groups, Lecture Notes in Math., vol. 414, Springer-Verlag, Berlin and New York, 1974. MR 376696
  • 15. T. Kambayashi, On the absence of nontrivial separable forms of the affine plane, J. Algebra 35 (1975), 449-456. MR 369380
  • 16. T. Kambayashi and M. Miyanishi, On flat fibrations by the affine line, Illinois J. Math. 22 (1978), no. 4, 662–671. MR 503968
  • 17. T. Kambayashi and M. Miyanishi, On forms of the affine line over a field, Lectures in Math., Kyoto Univ., Vol. 10. Tokyo: Kinokuniya Bookstores, 1977. MR 466159
  • 18. T. Kambayashi, Automorphism group of a polynomial ring and algebraic group action on an affine space, J. Algebra 60 (1979), no. 2, 439–451. MR 549939, https://doi.org/10.1016/0021-8693(79)90092-9
  • 19. T. Kambayashi, On Fujita's strong cancellation theorem for the affine plane, J. Fac. Sci. Univ. Tokyo (Sect. 1A) (to appear).
  • 20. M. Miyanishi, An algebraic characterization of the affine plane, J. Math. Kyoto Univ. 15 (1975), 169-184. MR 419460
  • 21. M. Miyanishi, Unirational quasi-elliptic surfaces in characteristic 3, Osaka J. Math. 13 (1976), 513-522. MR 437547
  • 22. Masayoshi Miyanishi, Unirational quasi-elliptic surfaces, Japan. J. Math. (N.S.) 3 (1977), no. 2, 395–416. MR 529285
  • 23. Masayoshi Miyanishi and Tohru Sugie, Affine surfaces containing cylinderlike open sets, J. Math. Kyoto Univ. 20 (1980), no. 1, 11–42. MR 564667, https://doi.org/10.1215/kjm/1250522319
  • 24. T. T. Moh, On analytic irreducibility at ∞ of a pencil of curves, Proc. Amer. Math. Soc. 44 (1974), 22-24. MR 357409
  • 25. M. P. Murthy, Generators for certain ideals in regular rings of dimension three, Comment. Math. Helv. 47 (1972), 179-184. MR 319976
  • 26. M. Nagata, On automorphism group of k[x, y], Lectures in Math., Kyoto Univ., Vol. 5. Tokyo: Kinokuniya Bookstores, 1972. MR 337962
  • 27. D. Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167-171. MR 427303
  • 28. C. P. Ramanujam, A topological characterization of the affine plane as an algebraic variety, Ann. of Math. (2) 94 (1971), 69-88. MR 286801
  • 29. P. Russell, Forms of the affine line and its additive group, Pacific J. Math. 32 (1970), 527-539. MR 265367
  • 30. Peter Russell, On affine-ruled rational surfaces, Math. Ann. 255 (1981), no. 3, 287–302. MR 615851, https://doi.org/10.1007/BF01450704
  • 31. U. Storch, Bemerking zu einem Satz von M. Kneser, Arch. Math. (Basel) 23 (1972), 403-404. MR 321921
  • 32. A. A. Suslin, On projective modules over polynomial rings, Math. USSR Sb. 22 (1974). MR 344238
  • 33. W. van der Kulk, On polynomial rings in two variables. Nieuw Archief voor Wiskunde (3) 1 (1953), 33-41. MR 54574

Review Information:

Reviewer: T. Kambayashi
Journal: Bull. Amer. Math. Soc. 4 (1981), 239-246
DOI: https://doi.org/10.1090/S0273-0979-1981-14896-5
American Mathematical Society