Details:
Title  The argument cycle and the coamoeba.  Author(s)  Petter Johansson  Type  Article in Journal  Abstract  We 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.  Keywords  coamoeba, initial form, Gröbner basis, degree of a continuous mapping, hyperplane arrangement,  ISSN  17476933; 17476941/e 
URL 
http://www.tandfonline.com/doi/abs/10.1080/17476933.2011.592581 
Language  English  Journal  Complex Var. Elliptic Equ.  Volume  58  Number  3  Pages  373384  Publisher  Taylor & Francis, Abingdon, Oxfordshire  Year  2013  Edition  0  Translation 
No  Refereed 
No 
