Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A unicity theorem for meromorphic mappings between algebraic varieties
HTML articles powered by AMS MathViewer

by S. J. Drouilhet PDF
Trans. Amer. Math. Soc. 265 (1981), 349-358 Request permission

Abstract:

Using the techniques of value distribution theory in several complex variables, we obtain a theorem which can be used to determine whether two nondegenerate meromorphic mappings from an affine algebraic variety to a projective algebraic variety of the same or lower dimension are identical. The theorem generalizes a result of $R$. Nevanlinna in one complex variable.
References
    J. A. Carlson, Personal correspondence. H. Cartan, Sur quelques théorèmes de M. R. Nevanlinna, C. R. Acad. Sci. Paris 185 (1927), 1253-1254. —, Un nouveau théorème d’unicité relatif aux fonctions méromorphes, C. R. Acad. Sci. Paris 188 (1929), 301-303. —, Sur les zéros des combinaisons linéaires de $p$ fonctions holomorphes données, Mathematica (Cluj) 7 (1933), 5-31.
  • S. J. Drouilhet, A unicity theorem for equidimensional holomorphic maps, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 2, Williams Coll., Williamstown, Mass., 1975) Amer. Math. Soc., Providence, R.I., 1977, pp. 237–238. MR 0450625
  • Hirotaka Fujimoto, The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J. 58 (1975), 1–23. MR 393586
  • Hirotaka Fujimoto, A uniqueness theorem of algebraically non-degenerate meromorphic maps into $P^{N}(C)$, Nagoya Math. J. 64 (1976), 117–147. MR 435453
  • Hirotaka Fujimoto, Remarks to the uniqueness problem of meromorphic maps into $P^{N}(\textbf {C})$. I, II, Nagoya Math. J. 71 (1978), 13–24, 25–41. MR 508993
  • Hirotaka Fujimoto, Remarks to the uniqueness problem of meromorphic maps into $P^{N}(\textbf {C})$. III, Nagoya Math. J. 75 (1979), 71–85. MR 542189
  • Phillip Griffiths and James King, Nevanlinna theory and holomorphic mappings between algebraic varieties, Acta Math. 130 (1973), 145–220. MR 427690, DOI 10.1007/BF02392265
  • R. C. Gunning, Lectures on Riemann surfaces, Princeton Mathematical Notes, Princeton University Press, Princeton, N.J., 1966. MR 0207977
  • Rolf Nevanlinna, Einige Eindeutigkeitssätze in der Theorie der Meromorphen Funktionen, Acta Math. 48 (1926), no. 3-4, 367–391 (German). MR 1555233, DOI 10.1007/BF02565342
  • —, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Gauthier-Villars, Paris, 1929.
  • Edwardine Michele Schmid, Some theorems on value distributions of meromorphic functions, Math. Z. 120 (1971), 61–92. MR 284583, DOI 10.1007/BF01109717
  • Bernard Shiffman, Nevanlinna defect relations for singular divisors, Invent. Math. 31 (1975), no. 2, 155–182. MR 430325, DOI 10.1007/BF01404113
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 32H30, 30D35
  • Retrieve articles in all journals with MSC: 32H30, 30D35
Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 265 (1981), 349-358
  • MSC: Primary 32H30; Secondary 30D35
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0610953-7
  • MathSciNet review: 610953