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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Tropical bases by regular projections


Authors: Kerstin Hept and Thorsten Theobald
Journal: Proc. Amer. Math. Soc. 137 (2009), 2233-2241
MSC (2000): Primary 13P10, 14Q99
Published electronically: February 18, 2009
MathSciNet review: 2495256
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Abstract: We consider the tropical variety $ \mathcal{T}(I)$ of a prime ideal $ I$ generated by the polynomials $ f_1, \ldots, f_r$ and revisit the regular projection technique introduced by Bieri and Groves from a computational point of view. In particular, we show that $ I$ has a short tropical basis of cardinality at most $ r+ \textrm{codim} I+1$ at the price of increased degrees, and we provide a computational description of these bases.


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Additional Information

Kerstin Hept
Affiliation: FB 12 – Institut für Mathematik, J.W. Goethe-Universität, Postfach 111932, D-60054 Frankfurt am Main, Germany
Email: hept@math.uni-frankfurt.de

Thorsten Theobald
Affiliation: FB 12 – Institut für Mathematik, J.W. Goethe-Universität, Postfach 111932, D-60054 Frankfurt am Main, Germany
Email: theobald@math.uni-frankfurt.de

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09843-8
PII: S 0002-9939(09)09843-8
Keywords: Tropical geometry, tropical variety, tropical basis, Bieri-Groves Theorem.
Received by editor(s): September 21, 2007
Received by editor(s) in revised form: September 29, 2008
Published electronically: February 18, 2009
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2009 American Mathematical Society