Details:
Title  Real radical initial ideals  Author(s)  Cynthia Vinzant  Type  Article in Journal  Abstract  We 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].  Keywords  Real algebraic geometry, Tropical geometry, Initial ideals, Semialgebraic sets, Preorders, Quadractic modules  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869311006971 
Language  English  Journal  Journal of Algebra  Volume  352  Number  1  Pages  392  407  Year  2012  Edition  0  Translation 
No  Refereed 
No 
