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Describing
amoebas
Mounir Nisse and Frank Sottile |
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Vol. 317 (2022), No. 1, 187–205
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Abstract |
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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 results and posing problems for further study. These problems include determining the dimension of an amoeba, describing an amoeba as a semialgebraic set, and identifying varieties whose amoebas are a finite intersection of amoebas of hypersurfaces. We show that an amoeba which is not of full dimension is not such a finite intersection if its variety is nondegenerate and we describe amoebas of lines as explicit semialgebraic sets. |
Keywords
amoeba, coamoeba, tropical geometry
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Mathematical Subject Classification
Primary: 14T99, 14T05, 32A60
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Milestones
Received: 16 February 2021
Revised: 25 June 2021
Accepted: 2 July 2021
Published: 19 June 2022
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Authors |
| Mounir Nisse | |
| Department of Mathematics Xiamen University Malaysia Sepang Malaysia |
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| Frank Sottile | |
| Department of Mathematics Texas A&M University College Station, TX United States |
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