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On the topology of the coamoeba
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we study the topology and geometry of the coamoeba of an algebraic variety V. The strategy that we use is to relate the coamoebas corresponding to the initial varieties of V to the coamoeba of V. We also define an analogue of the Ronkin function for the coamoeba and give an explicit formula for it.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University , 2014. , 36 p.
Keyword [en]
Coamoeba, Ronkin function
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-103125ISBN: 978-91-7447-933-1 (print)OAI: oai:DiVA.org:su-103125DiVA: diva2:715770
Public defence
2014-06-12, sal 14 hus 5 Kräftriket, Roslagsvägen 101, Stockholm, 13:15 (English)
Opponent
Supervisors
Available from: 2014-05-22 Created: 2014-05-06 Last updated: 2014-05-22Bibliographically approved
List of papers
1. A Ronkin type function for coamoebas
Open this publication in new window or tab >>A Ronkin type function for coamoebas
(English)Manuscript (preprint) (Other academic)
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:su:diva-103123 (URN)
Available from: 2014-05-06 Created: 2014-05-06 Last updated: 2014-05-06
2. The argument cycle and the coamoeba
Open this publication in new window or tab >>The argument cycle and the coamoeba
2013 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 58, no 3, 373-384 p.Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
coamoeba, initial form, Grobner basis, degree of a continuous mapping, hyperplane arrangement, 14M25, 14M10
National Category
Mathematics
Identifiers
urn:nbn:se:su:diva-88283 (URN)10.1080/17476933.2011.592581 (DOI)000313420500007 ()
Note

AuthorCount:1;

Available from: 2013-03-12 Created: 2013-03-12 Last updated: 2017-12-06Bibliographically approved
3. Coamoebas and line arrangements in dimension two
Open this publication in new window or tab >>Coamoebas and line arrangements in dimension two
(English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823Article in journal (Refereed) In press
Keyword
Coamoeba
National Category
Geometry
Identifiers
urn:nbn:se:su:diva-103121 (URN)
Available from: 2014-05-06 Created: 2014-05-06 Last updated: 2017-12-05
4. Some results on amoebas and coamoebas of affine spaces
Open this publication in new window or tab >>Some results on amoebas and coamoebas of affine spaces
(English)Manuscript (preprint) (Other academic)
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:su:diva-103122 (URN)
Available from: 2014-05-06 Created: 2014-05-06 Last updated: 2014-05-06

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