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Book Review
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Book Information
Author(s):
Robert S. Rumely
Title:
Capacity theory on algebraic curves
Additional book information:
Lecture Notes in Mathematics, vol. 1378, Springer-Verlag, Berlin, Heidelberg, and
New York, 1989, 437 pp., US$37.50. ISBN 3-540-51410-4
References:
- [1]
- D. Cantor, On an extension of the definition of the transfinite diameter and some applications, J. Reine Angew. Math. \textbf{316} (1980), 160--207.
- [2]
- T. Chinburg, Capacity theory on varieties, Compositio Math. \textbf{80} (1991), 75--84.
- [3]
- G. Faltings, The general case of S. Lang's Conjecture, preprint, 1991.
- [4]
- M. Fekete, \"Uber die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. \textbf{17} (1923), 228--249.
- [5]
- M. Fekete and G. Szeg\"o, On algebraic equations with integral coefficients whose roots belong to a given point set, Math. Z. \textbf{63} (1955), 158--172.
- [6]
- H. Gillet and C. Soul\'e, Arithmetic intersection theory, Inst. Hautes \'Etudes Sci. Publ. Math. \textbf{72} (1990), 93--174.
- [7]
- E. Kani, \emph{theory on curves}.
- [8]
- R. Rumely, \emph{Capacity theory on algebraic curves and canonical heights}, $12^e$ Ann\'ee, 1984/1985, Paris.
- [9]
- R. Rumely, On the relation between Cantor's capacity and Chinburg's sectional capacity, preprint (1990).
- [10]
- B. A. Taylor, {\rm book review of } Capacities in complex analysis, by U. Cegrell, Bull. Amer. Math. Soc. (N.S.) \textbf{24} (1991), 213--216.
- [11]
- P. Vojta, Siegel's theorem in the compact case, Annals of Math. \textbf{133} (1991), 509--548.
- [12]
- S. Zhang, Positive line bundles on arithmetic surfaces, Columbia Univ. Thesis, 1991.
Additional Information:
Reviewer(s):
Ted
Chinburg
Review Information:
Journal:
Bull. Amer. Math. Soc.
26
(1992),
332-336.
DOI:
10.1090/S0273-0979-1992-00262-8
PII:
S 0273-0979(1992)00262-8
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