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Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

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 transfinite diameter and some applications, J. Reine Angew. Math. 316 (1980), 160-207. MR 581330 (81m:12002)

[2]
T. Chinburg, Capacity theory on varieties, Compositio Math. 80 (1991), 75-84. MR 1127060 (93d:14039)

[3]
G. Faltings, The general case of S. Lang's Conjecture, preprint, 1991.

[4]
M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), 228-249. MR 1544613

[5]
M. Fekete and G. Szegö, On algebraic equations with integral coefficients whose roots belong to a given point set, Math. Z. 63 (1955), 158-172. MR 0072941 (17:355a)

[6]
H. Gillet and C. Soulé, Arithmetic intersection theory, Inst. Hautes Études Sci. Publ. Math. 72 (1990), 93-174. MR 1087394 (92d:14016)

[7]
E. Kani, Potential theory on curves, Proc. Internat. Conf. Number Theory, Quebec, 1987 (to appear). MR 1024584 (91e:14020)

[8]
R. Rumely, Capacity theory on algebraic curves and canonical heights, No. 22 Fasc. 2, Groupe d'étude d'Analyse ultramétrique (Y. Amice, G. Christol, P. Robba, eds.) 12 $ ^{\emph{e}}$ Année, 1984/1985, Paris. MR 848999 (87i:11077)

[9]
-, On the relation between Cantor's capacity and Chinburg's sectional capacity, preprint (1990).

[10]
B. A. Taylor, book review of Capacities in complex analysis, by U. Cegrell, Bull. Amer. Math. Soc. (N.S.) 24 (1991), 213-216. MR 1567903

[11]
P. Vojta, Siegel's theorem in the compact case, Annals of Math. 133 (1991), 509-548. MR 1109352 (93d:11065)

[12]
S. Zhang, Positive line bundles on arithmetic surfaces, Columbia Univ. Thesis, 1991. MR 1189866 (93j:14024)

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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