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Mathematics > Algebraic Geometry

arXiv:1805.00273 (math)
[Submitted on 1 May 2018 (v1), last revised 16 Feb 2021 (this version, v3)]

Title:Describing Amoebas

Authors:Mounir Nisse, Frank Sottile
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Abstract:An amoeba is the image of a subvariety of an algebraic torus under the logarithmic moment map. We consider some qualitative aspects of amoebas, establishing some results and posing problems for further study. These problems include determining the dimension of an amoeba, describing an amoeba as a semi-algebraic set, and identifying varieties whose amoebas are a finite intersection of amoebas of hypersurfaces. We show that an amoeba that is not of full dimension is not such a finite intersection if its variety is nondegenerate and we describe amoebas of lines as explicit semi-algebraic sets.
Comments: 16 pages, 3 figures
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14T99
Cite as: arXiv:1805.00273 [math.AG]
  (or arXiv:1805.00273v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.00273
Journal reference: Pacific J. Math. 317 (2022) 187-205
Related DOI: https://doi.org/10.2140/pjm.2022.317.187

Submission history

From: Frank Sottile [view email]
[v1] Tue, 1 May 2018 11:22:23 UTC (45 KB)
[v2] Thu, 20 Dec 2018 15:34:51 UTC (44 KB)
[v3] Tue, 16 Feb 2021 17:31:55 UTC (48 KB)
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