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Book Information

Author(s): 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

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, Bombay, 1977. 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.: T. Fujita, On Zariski problem, Proc. Japan Acad. 55-A (1979), 106-110. MR 531454
9.: R. Ganong, On plane curves with one place at infinity, J. Reine Angew Math 307/308 (1979), 173-193. MR 534219
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), 662-667. 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), 439-451. MR 549939
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.: M. Miyanishi, Unirational quasi-elliptic surfaces, Japan. J. Math. (N.S.) 3 (1977), 395-416. MR 529285
23.: M. Miyanishi and T. Sugie, Affine surfaces containing cylinderlike open sets, J. Math. Kyoto Univ. 20 (1980), 11-42. MR 564667
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.: P. Russell, On affine-ruled rational surfaces, Math. Ann. (to appear). MR 615851
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:
Journal: Bull. Amer. Math. Soc. 4 (1981), 239-246.
DOI: 10.1090/S0273-0979-1981-14896-5
PII: S 0273-0979(1981)14896-5

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ISSN 1088-9485(e) ISSN 0273-0979(p)

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