The degree of a tropical basis
Authors:
Michael Joswig and Benjamin Schröter
Journal:
Proc. Amer. Math. Soc. 146 (2018), 961-970
MSC (2010):
Primary 13P10, 14T05
DOI:
https://doi.org/10.1090/proc/13787
Published electronically:
October 5, 2017
MathSciNet review:
3750210
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Abstract | References | Similar Articles | Additional Information
Abstract: We give an explicit upper bound for the degree of a tropical basis of a homogeneous polynomial ideal. As an application $f$-vectors of tropical varieties are discussed. Various examples illustrate differences between Gröbner and tropical bases.
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Additional Information
Michael Joswig
Affiliation:
Institut für Mathematik, TU Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
ORCID:
0000-0002-4974-9659
Email:
joswig@math.tu-berlin.de
Benjamin Schröter
Affiliation:
Institut für Mathematik, TU Berlin, Str. des 17. Juni 136, 10623 Berlin, Germany
Email:
schroeter@math.tu-berlin.de
Keywords:
Universal Gröbner bases,
$f$-vectors of tropical varieties
Received by editor(s):
December 1, 2015
Received by editor(s) in revised form:
April 19, 2017
Published electronically:
October 5, 2017
Additional Notes:
Research by the authors was carried out in the framework of Matheon supported by Einstein Foundation Berlin. Further support by Deutsche Forschungsgemeinschaft (SFB-TRR 109: “Discretization in Geometry and Dynamics” and SFB-TRR 195: “Symbolic Tools in Mathematics and their Application”) is gratefully acknowledged
Communicated by:
Irena Peeva
Article copyright:
© Copyright 2017
American Mathematical Society
