Amoebas of Maximal Area
2001 (English)In: International Mathematics Research Notices, ISSN 1687-0247, Vol. 9, 441-451 p.Article in journal (Refereed) Published
To any algebraic curve A in (C*)^2 one may associate a closed infinite region A in R^2 called the amoeba of A. The amoebas of different curves of the same degree come in different shapes and sizes. All amoebas in (R*)^2 have finite area and, furthermore, there is an upper bound on the area in terms of the degree of the curve. The subject of this paper is the curves in (C*)^2 whose amoebas are of the maximal area. We show that up to multiplication by a constant in (C*)^2, such curves are defined over R and, furthermore, that their real loci are isotopic to so-called Harnack curves.
Place, publisher, year, edition, pages
2001. Vol. 9, 441-451 p.
IdentifiersURN: urn:nbn:se:su:diva-20271DOI: doi:10.1155/S107379280100023XOAI: oai:DiVA.org:su-20271DiVA: diva2:186797