Explicit computation of certain Arakelov-Green functions


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Cinkir Z.

KYOTO JOURNAL OF MATHEMATICS, vol.54, no.4, pp.759-774, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 4
  • Publication Date: 2014
  • Doi Number: 10.1215/21562261-2801804
  • Title of Journal : KYOTO JOURNAL OF MATHEMATICS
  • Page Numbers: pp.759-774

Abstract

Arakelov-Green functions defined on metrized graphs have an important role in relating arithmetical problems on algebraic curves to graph-theoretical problems. In this paper, we clarify the combinatorial interpretation of certain Arakelov-Green functions by using electric circuit theory. The formulas we give clearly show that such functions are piecewisely defined, and each piece is a linear or quadratic function on each pair of edges of metrized graphs. These formulas lead to an efficient algorithm for explicit computation of Arakelov-Green functions.