Bulletin of the American Mathematical Society

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Book Information:

Author: Makoto Namba
Title: Families of meromorphic functions on compact Riemann surfaces
Additional book information: Lecture Notes in Math., vol. 767, Springer-Verlag, Berlin and New York, 1979, xii + 284 pp., $16.30.

Enrico Arbarello, Weierstrass points and moduli of curves, Compositio Math. 29 (1974), 325–342. MR 360601

2.

A. Brill and M. Noether, Ueber die algebraischen Funktionen und ihre Anwendungen in der Geometrie, Math. Ann. 7 (1874), 269-310.

Clifford J. Earle, Families of Riemann surfaces and Jacobi varieties, Ann. of Math. (2) 107 (1978), no. 2, 255–286. MR 499328, DOI 10.2307/1971144

Hershel M. Farkas, Special divisors on compact Riemann surfaces, Proc. Amer. Math. Soc. 19 (1968), 315–318. MR 222283, DOI 10.1090/S0002-9939-1968-0222283-5

5.

P. Griffiths, E. Arbarello, M. Cornalba and J. Harris, Ann. of Math. Studies, Princeton Univ. Press, Princeton, N. J. (to appear).

R. C. Gunning, Lectures on Riemann surfaces, Jacobi varieties, Mathematical Notes, No. 12, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0357407

Richard S. Hamilton, Non-hyperelliptic Riemann surfaces, J. Differential Geometry 3 (1969), 95–101. MR 249604

8.

S. H. Katz, Thesis, Princeton University, 1980.

9.

G. Kempf, Schubert methods with an application to algebraic curves, Publ. Math. Centrum, Amsterdam, 1970.

George Kempf, On the geometry of a theorem of Riemann, Ann. of Math. (2) 98 (1973), 178–185. MR 349687, DOI 10.2307/1970910

Steven L. Kleiman and Dan Laksov, Another proof of the existence of special divisors, Acta Math. 132 (1974), 163–176. MR 357398, DOI 10.1007/BF02392112

Steven L. Kleiman, $r$-special subschemes and an argument of Severi’s, Advances in Math. 22 (1976), no. 1, 1–31. MR 435071, DOI 10.1016/0001-8708(76)90135-3

R. F. Lax, On the dimension of varieties of special divisors, Trans. Amer. Math. Soc. 203 (1975), 141–159. MR 360602, DOI 10.1090/S0002-9947-1975-0360602-8

R. F. Lax, Weierstrass points of the universal curve, Math. Ann. 216 (1975), 35–42. MR 384809, DOI 10.1007/BF02547970

Joseph Lewittes, Riemann surfaces and the theta function, Acta Math. 111 (1964), 37–61. MR 156964, DOI 10.1007/BF02391007

G. Martens, Funktionen von vorgegebener Ordnung auf komplexen Kurven, J. Reine Angew. Math. 320 (1980), 68–85 (German). MR 592143, DOI 10.1515/crll.1980.320.68

Henrik H. Martens, On the varieties of special divisors on a curve, J. Reine Angew. Math. 227 (1967), 111–120. MR 215847, DOI 10.1515/crll.1967.227.111

Henrik H. Martens, On the partial derivatives of theta functions, Comment. Math. Helv. 48 (1973), 394–408. MR 344259, DOI 10.1007/BF02566132

A. L. Mayer, Special divisors and the Jacobian variety, Math. Ann. 153 (1964), 163–167. MR 164969, DOI 10.1007/BF01360314

Theodor Meis, Die minimale Blätterzahl der Konkretisierungen einer kompakten Riemannschen Fläche, Schr. Math. Inst. Univ. Münster 16 (1960), 61 (German). MR 147643

David Mumford, Prym varieties. I, Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 325–350. MR 0379510

David Mumford, Curves and their Jacobians, University of Michigan Press, Ann Arbor, Mich., 1975. MR 0419430

H. E. Rauch, Weierstrass points, branch points, and moduli of Riemann surfaces, Comm. Pure Appl. Math. 12 (1959), 543–560. MR 110798, DOI 10.1002/cpa.3160120310

H. E. Rauch, A transcendental view of the space of algebraic Riemann surfaces, Bull. Amer. Math. Soc. 71 (1965), 1–39. MR 213543, DOI 10.1090/S0002-9904-1965-11225-3

André Weil, Zum Beweis des Torellischen Satzes, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. IIa. 1957 (1957), 33–53 (German). MR 0089483

1.

E. Arbarello, Weierstrass points and moduli of curves, Compositio Math. 29 (1974), 325-342. MR 0360601

2.

A. Brill and M. Noether, Ueber die algebraischen Funktionen und ihre Anwendungen in der Geometrie, Math. Ann. 7 (1874), 269-310.

3.

C. J. Earle, Families of Riemann surfaces and Jacobi varieties, Ann. of Math. (2) 107 (1978), 255-286. MR 499328

4.

H. Farkas, Special divisors on compact Riemann surfaces, Proc. Amer. Math. Soc. 19 (1968), 315-318; Special divisors and analytic subloci of Teichmueller space, Amer. J. Math. 88 (1966), 881-901. MR 222283

5.

P. Griffiths, E. Arbarello, M. Cornalba and J. Harris, Ann. of Math. Studies, Princeton Univ. Press, Princeton, N. J. (to appear).

6.

R. C. Gunning, Lectures on Riemann surfaces: Jacobi varieties, Princeton Univ. Press, Princeton, N. J., 1972. MR 357407

7.

R. S. Hamilton, Non hyperelliptic Riemann surfaces, J. Differential Geometry 3 (1969), 95-101. MR 249604

8.

S. H. Katz, Thesis, Princeton University, 1980.

9.

G. Kempf, Schubert methods with an application to algebraic curves, Publ. Math. Centrum, Amsterdam, 1970.

10.

G. Kempf, On the geometry of a theorem of Riemann, Ann. of Math. (2) 98 (1973), 178-185. MR 349687

11.

S. Kleiman and D. Laksov, On the existence of special divisors, Amer. J. Math. 94 (1972), 431-436; Another proof of the existence of special divisors, Acta. Math. 132 (1974), 163-176. MR 357398

12.

S. Kleiman, r-special subschemes and an argument of Severi's (Appendix by D. Laksov), Adv. in Math. 22 (1976), 1-31. MR 435071

13.

R. F. Lax, On the dimension of varieties of special divisors. I, Trans. Amer. Math. Soc. 203 (1975), 141-159; II, Illinois J. Math. 19 (1975), 318-324. MR 360602

14.

R. F. Lax, Weierstrass points of the universal curve, Math. Ann. 216 (1975), 35-42. MR 384809

15.

J. Lewittes, Riemann surfaces and the theta function, Acta Math. 111 (1964), 37-61. MR 156964

16.

G. Martens, Funktionen von vorgegebener Ordnung auf komplexen Kurven, J. Reine Angew. Math. (to appear). MR 592143

17.

H. H. Martens, On the varieties of special divisors on a curve, J. Reine Angew. Math. 227 (1967), 111-120; Varieties of special divisors on a curve. II, J. Reine Angew. Math. 233 (1968), 89-100. MR 215847

18.

H. H. Martens, On the partial derivatives of theta functions, Comment. Math. Helv. 48 (1973), 394-408. MR 344259

19.

A. L. Mayer, Special divisors and the Jacobian variety, Math. Ann. 153 (1964), 163-167. MR 164969

20.

T. Meis, Die minimale Blätterzahl der Konkretisierung einer kompakten Riemannschen Fläche, Schr. Math. Inst. Univ. Münster, No. 16 (1960), 61 pp. MR 147643

21.

D. Mumford, Prym varieties. I, Contributions to Analysis, Academic Press, New York, 1974, pp. 325-350. MR 379510

22.

D. Mumford, Curves and their Jacobians, Univ. of Mich. Press, Ann Arbor, Michigan, 1975. MR 419430

23.

H. E. Rauch, Weierstrass points, branch points, and moduli of Riemann surfaces, Comm. Pure Appl. Math. 12 (1959), 543-560. MR 110798

24.

H. E. Rauch, A transcendental view of the space of algebraic Riemann surfaces, Bull. Amer. Math. Soc. 71 (1965), 1-39. MR 213543

25.

A. Weil, Zum Beweis des Torellischen Satz, Nachr. Akad. Wiss. Göttingen (1957), 33-53. MR 89483