The argument cycle and the coamoeba
2013 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 58, no 3, 373-384 p.Article in journal (Refereed) Published
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 Grobner 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 ? on the n:th torus. For this purpose, we associate a certain algebraic cycle, the argument cycle, to V and ? , and study its homology. In particular, we give a method to approximate the coamoeba when n?=?2.
Place, publisher, year, edition, pages
2013. Vol. 58, no 3, 373-384 p.
coamoeba, initial form, Grobner basis, degree of a continuous mapping, hyperplane arrangement, 14M25, 14M10
IdentifiersURN: urn:nbn:se:su:diva-88283DOI: 10.1080/17476933.2011.592581ISI: 000313420500007OAI: oai:DiVA.org:su-88283DiVA: diva2:610714