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TitleReal radical initial ideals
Author(s) Cynthia Vinzant
TypeArticle in Journal
AbstractWe explore the consequences of an ideal I ⊂ R [ x 1 , , x n ] having a real radical initial ideal, both for the geometry of the real variety of I and as an application to sums of squares representations of polynomials. We show that if in w ( I ) is real radical for a vector w in the tropical variety, then w is in the logarithmic set of the real variety. We also give algebraic sufficient conditions for w to be in the logarithmic limit set of a more general semialgebraic set. If in addition w ∈ ( R > 0 ) n , then the corresponding quadratic module is stable. In particular, if in w ( I ) is real radical for some w ∈ ( R > 0 ) n then ∑ R [ x 1 , , x n ] 2 + I is stable. This provides a method for checking the conditions for stability given by Powers and Scheiderer (2001) [PS].
KeywordsReal algebraic geometry, Tropical geometry, Initial ideals, Semialgebraic sets, Preorders, Quadractic modules
ISSN0021-8693
URL http://www.sciencedirect.com/science/article/pii/S0021869311006971
LanguageEnglish
JournalJournal of Algebra
Volume352
Number1
Pages392 - 407
Year2012
Edition0
Translation No
Refereed No
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