# zbMATH — the first resource for mathematics

On the relation between Cantor’s capacity and the sectional capacity. (English) Zbl 0808.14023
The author proves some theorems concerning T. Chinberg’s sectional capacity for algebraic varieties. In the case of algebraic curves this capacity is related to another kind of capacity which was introduced by D. Cantor and the author. A quadratic form which determines both kind of capacities is given.
In the first part the definitions of the two notions of capacity are recalled. In the main part the author gives a detailed explanation of the machinery which is necessary to prove the theorem. – In a final section two applications of the theorem are proved: a base-change formula and a pullback formula.

##### MSC:
 14H30 Coverings of curves, fundamental group 30F10 Compact Riemann surfaces and uniformization
##### Keywords:
sectional capacity
Full Text:
##### References:
 [1] D. G. Cantor, On an extension of the definition of transfinite diameter and some applications , J. Reine Angew. Math. 316 (1980), 160-207. · Zbl 0445.30019 [2] T. Chinburg, Capacity theory on varieties , Compositio Math. 80 (1991), no. 1, 75-84. · Zbl 0761.11028 [3] M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten , Math. Z. 17 (1923), 228-249. · JFM 49.0047.01 [4] 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. · Zbl 0066.27002 [5] R. S. Rumely, Capacity theory on algebraic curves , Lecture Notes in Mathematics, vol. 1378, Springer-Verlag, Berlin, 1989. · Zbl 0679.14012 [6] A. Weil, Foundations of Algebraic Geometry , Amer. Math. Soc. Colloq. Publ., vol. 29, American Mathematical Society, Providence, R.I., 1962. · Zbl 0063.08198
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.