Bulletin of the American Mathematical Society

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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.

Shreeram S. Abhyankar, Algebraic space curves, Séminaire de Mathématiques Supérieures, No. 43 (Été 1970), Les Presses de l’Université de Montréal, Montreal, Que., 1971. MR 0399109

Shreeram S. Abhyankar, William Heinzer, and Paul Eakin, On the uniqueness of the coefficient ring in a polynomial ring, J. Algebra 23 (1972), 310–342. MR 306173, DOI 10.1016/0021-8693(72)90134-2

Shreeram S. Abhyankar and Tzuong Tsieng Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975), 148–166. MR 379502

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

Enrico Bombieri and Dale Husemoller, Classification and embeddings of surfaces, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 329–420. MR 0506292

Paul Eakin and William Heinzer, A cancellation problem for rings, Conference on Commutative Algebra (Univ. Kansas, Lawrence, Kan., 1972), Lecture Notes in Math., Vol. 311, Springer, Berlin, 1973, pp. 61–77. MR 0349664

David Eisenbud and E. Graham Evans Jr., Every algebraic set in $n$-space is the intersection of $n$ hypersurfaces, Invent. Math. 19 (1973), 107–112. MR 327783, DOI 10.1007/BF01418923

Takao Fujita, On Zariski problem, Proc. Japan Acad. Ser. A Math. Sci. 55 (1979), no. 3, 106–110. MR 531454

Richard Ganong, On plane curves with one place at infinity, J. Reine Angew. Math. 307(308) (1979), 173–193. MR 534219, DOI 10.1515/crll.1979.307-308.173

10.

A. Grothendieck, Eléments de Géométrie Algébrique, Publ. Math. Inst. Hautes Étude Sci., 1960-1967.

M. Hochster, Nonuniqueness of coefficient rings in a polynomial ring, Proc. Amer. Math. Soc. 34 (1972), 81–82. MR 294325, DOI 10.1090/S0002-9939-1972-0294325-3

S. Iitaka, On logarithmic Kodaira dimension of algebraic varieties, Complex analysis and algebraic geometry, Iwanami Shoten, Tokyo, 1977, pp. 175–189. MR 0569688

Shigeru Iitaka, Logarithmic forms of algebraic varieties, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), no. 3, 525–544. MR 429884

Tatsuji Kambayashi, Masayoshi Miyanishi, and Mitsuhiro Takeuchi, Unipotent algebraic groups, Lecture Notes in Mathematics, Vol. 414, Springer-Verlag, Berlin-New York, 1974. MR 0376696

T. Kambayashi, On the absence of nontrivial separable forms of the affine plane, J. Algebra 35 (1975), 449–456. MR 369380, DOI 10.1016/0021-8693(75)90058-7

T. Kambayashi and M. Miyanishi, On flat fibrations by the affine line, Illinois J. Math. 22 (1978), no. 4, 662–671. MR 503968

Tatsuji Kambayashi and Masayoshi Miyanishi, On forms of the affine line over a field, Lectures in Mathematics, Kyoto University, No. 10, Kinokuniya Book Store Co., Ltd., Tokyo, 1977. MR 0466159

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, DOI 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).

Masayoshi Miyanishi, An algebraic characterization of the affine plane, J. Math. Kyoto Univ. 15 (1975), 169–184. MR 419460, DOI 10.1215/kjm/1250523123

Masayoshi Miyanishi, Unirational quasi-elliptic surfaces in characteristic $3$, Osaka Math. J. 13 (1976), no. 3, 513–522. MR 437547

Masayoshi Miyanishi, Unirational quasi-elliptic surfaces, Japan. J. Math. (N.S.) 3 (1977), no. 2, 395–416. MR 529285, DOI 10.4099/math1924.3.395

Masayoshi Miyanishi and Tohru Sugie, Affine surfaces containing cylinderlike open sets, J. Math. Kyoto Univ. 20 (1980), no. 1, 11–42. MR 564667, DOI 10.1215/kjm/1250522319

T. T. Moh, On analytic irreducibility at $\infty$ of a pencil of curves, Proc. Amer. Math. Soc. 44 (1974), 22–24. MR 357409, DOI 10.1090/S0002-9939-1974-0357409-9

M. Pavanan Murthy, Generators for certain ideals in regular rings of dimension three, Comment. Math. Helv. 47 (1972), 179–184. MR 319976, DOI 10.1007/BF02566796

Masayoshi Nagata, On automorphism group of $k[x,\,y]$, Kinokuniya Book Store Co., Ltd., Tokyo, 1972. Department of Mathematics, Kyoto University, Lectures in Mathematics, No. 5. MR 0337962

Daniel Quillen, Projective modules over polynomial rings, Invent. Math. 36 (1976), 167–171. MR 427303, DOI 10.1007/BF01390008

C. P. Ramanujam, A topological characterisation of the affine plane as an algebraic variety, Ann. of Math. (2) 94 (1971), 69–88. MR 286801, DOI 10.2307/1970735

Peter Russell, Forms of the affine line and its additive group, Pacific J. Math. 32 (1970), 527–539. MR 265367

Peter Russell, On affine-ruled rational surfaces, Math. Ann. 255 (1981), no. 3, 287–302. MR 615851, DOI 10.1007/BF01450704

Uwe Storch, Bemerkung zu einem Satz von M. Kneser, Arch. Math. (Basel) 23 (1972), 403–404 (German). MR 321921, DOI 10.1007/BF01304903

A. A. Suslin, Projective modules over polynomial rings, Mat. Sb. (N.S.) 93(135) (1974), 588–595, 630 (Russian). MR 0344238

W. van der Kulk, On polynomial rings in two variables, Nieuw Arch. Wisk. (3) 1 (1953), 33–41. MR 54574

1.

S. S. Abhyankar, Algebraic space curves, Séminaire de Mathématiques Supérieures, Université de Montréal, 1970. MR 0399109

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