A hypersurface defect relation for a class of meromorphic maps
HTML articles powered by AMS MathViewer
- by Aldo Biancofiore PDF
- Trans. Amer. Math. Soc. 270 (1982), 47-60 Request permission
Abstract:
Let ${D_1}, \ldots ,{D_q}$ be hypersurfaces of degree $p$ in ${{\mathbf {P}}_n}$ with normal crossings. We prove for a certain class of meromorphic maps $f:{{\mathbf {C}}^m} \to {{\mathbf {P}}_n}$ a defect relation ${\delta _f}\left ( {{D_1}} \right ) + \cdots + {\delta _f}({D_q}) \leqslant (n + 1)/p$ conjectured by Ph. Griffiths and B. Shiffman.References
- Lars V. Ahlfors, The theory of meromorphic curves, Acta Soc. Sci. Fennicae. Nova Ser. A 3 (1941), no. 4, 31. MR 4309 A. Biancofiore, A hypersurface defect relation for a class of meromorphic maps, Thesis, Univ. of Notre Dame, 1981.
- James Carlson and Phillip Griffiths, A defect relation for equidimensional holomorphic mappings between algebraic varieties, Ann. of Math. (2) 95 (1972), 557–584. MR 311935, DOI 10.2307/1970871 H. Cartan, Sur les zéros des combinaisons linéaires de $p$ fonctions holomorphes données, Mathematica (Cluj) 7 (1933), 80-103.
- Phillip A. Griffiths, Holomorphic mappings: Survey of some results and discussion of open problems, Bull. Amer. Math. Soc. 78 (1972), 374–382. MR 294718, DOI 10.1090/S0002-9904-1972-12905-7
- 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
- Seiki Mori, On the deficiencies of meromorphic mappings of $C^{n}$ into $P^{N}C$, Nagoya Math. J. 67 (1977), 165–176. MR 466644 R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions meromorphes, Gauthier-Villars, Paris, 1929.
- Bernard Shiffman, Holomorphic curves in algebraic manifolds, Bull. Amer. Math. Soc. 83 (1977), no. 4, 553–568. MR 440075, DOI 10.1090/S0002-9904-1977-14323-1
- Bernard Shiffman, On holomorphic curves and meromorphic maps in projective space, Indiana Univ. Math. J. 28 (1979), no. 4, 627–641. MR 542949, DOI 10.1512/iumj.1979.28.28044
- Wilhelm Stoll, Die beiden Hauptsätze der Wertverteilungstheorie bei Funktionen mehrerer komplexer Veränderlichen. I, Acta Math. 90 (1953), 1–115 (German). MR 76407, DOI 10.1007/BF02392435
- Al Vitter, The lemma of the logarithmic derivative in several complex variables, Duke Math. J. 44 (1977), no. 1, 89–104. MR 432924
- Hermann Weyl, Meromorphic Functions and Analytic Curves, Annals of Mathematics Studies, No. 12, Princeton University Press, Princeton, N. J., 1943. MR 0009057
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 270 (1982), 47-60
- MSC: Primary 32A22; Secondary 32H30
- DOI: https://doi.org/10.1090/S0002-9947-1982-0642329-1
- MathSciNet review: 642329