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Toric Degenerations of Polynomial Ideals and Geometric Localization of Fans

✍ Scribed by STÉPHANE COLLART; DANIEL MALL

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 580 KB
Volume: 24
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1996.0144

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✦ Synopsis

Toric degenerations of polynomial ideals occur if one allows certain partial term orders in the theory of Gröbner bases. We prove that the collection of toric degenerations of an ideal can be monotonically embedded into the complex closure of the Gröbner fan. A process of geometric localization on the Gröbner fan of the ideal yields the Gröbner fans of the toric degenerations.

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