Explicit computation of certain Arakelov-Green functions


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Cinkir Z.

KYOTO JOURNAL OF MATHEMATICS, cilt.54, ss.759-774, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 54 Konu: 4
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1215/21562261-2801804
  • Dergi Adı: KYOTO JOURNAL OF MATHEMATICS
  • Sayfa Sayısı: ss.759-774

Özet

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.