Abstract:
Derive an explicit integral formula for the amoeba-to-coamoeba mapping in the case of polynomials that define Harnack curves. As a consequence obtain an exact description of the coamoebas of such polynomials. This formula can be viewed as a generalization of the familiar law of cosines that is used for solving triangles.
Keywords:
Harnack curves, amoeba of polynomial, coamoeba of polynomial, Newton polygon, Ronkin function, law of cosines.
Received: 20.06.2016 Received in revised form: 20.06.2016 Accepted: 20.06.2016
Bibliographic databases:
Document Type:
Article
UDC:519.21
Language: English
Citation:
Mikael Passare, “The trigonometry of Harnack curves”, J. Sib. Fed. Univ. Math. Phys., 9:3 (2016), 347–352
\Bibitem{Pas16}
\by Mikael~Passare
\paper The trigonometry of Harnack curves
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 3
\pages 347--352
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\crossref{https://doi.org/10.17516/1997-1397-2016-9-3-347-352}
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Linking options:
https://www.mathnet.ru/eng/jsfu493
https://www.mathnet.ru/eng/jsfu/v9/i3/p347
This publication is cited in the following 4 articles:
Cédric Boutillier, David Cimasoni, Béatrice de Tilière, “Minimal bipartite dimers and higher genus Harnack curves”, Prob. Math. Phys., 4:1 (2023), 151
Cédric Boutillier, David Cimasoni, Béatrice de Tilière, “Elliptic Dimers on Minimal Graphs and Genus 1 Harnack Curves”, Commun. Math. Phys., 400:2 (2023), 1071
Vitaly A. Krasikov, “A Survey on Computational Aspects of Polynomial Amoebas”, Math.Comput.Sci., 17:3-4 (2023)
A. Lushin, D. Pochekutov, “Toric Cycles in the Complement to a Complex Curve in (C-X)(2)”, Math. Nachr., 292:12 (2019), 2654–2661
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