Tropical bases by regular projections
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- by Kerstin Hept and Thorsten Theobald
- Proc. Amer. Math. Soc. 137 (2009), 2233-2241
- DOI: https://doi.org/10.1090/S0002-9939-09-09843-8
- Published electronically: February 18, 2009
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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.References
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Bibliographic 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
- MR Author ID: 618735
- ORCID: 0000-0002-5769-0917
- Email: theobald@math.uni-frankfurt.de
- 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
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2233-2241
- MSC (2000): Primary 13P10, 14Q99
- DOI: https://doi.org/10.1090/S0002-9939-09-09843-8
- MathSciNet review: 2495256