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TitleThe argument cycle and the coamoeba.
Author(s) Petter Johansson
TypeArticle in Journal
AbstractWe investigate the coamoeba of a complex algebraic variety V ⊂ (ℂ*) n through the study of initial forms of the defining ideal. By use of a universal Gröbner basis, we prove that the closure of the coamoeba is included in the union of coamoebas corresponding to all initial ideals. We also study complete intersections V of dimension n/2 more closely to get a lower bound for the multiplicity in V of a given point θ on the n:th torus. For this purpose, we associate a certain algebraic cycle, the argument cycle, to V and θ , and study its homology. In particular, we give a method to approximate the coamoeba when n = 2.
Keywordscoamoeba, initial form, Gröbner basis, degree of a continuous mapping, hyperplane arrangement,
ISSN1747-6933; 1747-6941/e
URL http://www.tandfonline.com/doi/abs/10.1080/17476933.2011.592581
JournalComplex Var. Elliptic Equ.
PublisherTaylor & Francis, Abingdon, Oxfordshire
Translation No
Refereed No