Details:
Title  Termordering free involutive bases  Author(s)  Michela Ceria, Teo Mora, margherita Roggero  Type  Article in Journal  Abstract  Abstract In this paper, we consider a monomial ideal J ◃ P : = A [x_1, … , x_n] , over a commutative ring A, and we face the problem of the characterization for the family Mf(J) of all homogeneous ideals I ◃ P such that the Amodule P/I is free with basis given by the set of terms in the Gröbner escalier N(J) of J. This family is in general wider than that of the ideals having J as initial ideal w.r.t. any termordering, hence more suited to a computational approach to the study of Hilbert schemes. For this purpose, we exploit and enhance the concepts of multiplicative variables, complete sets and involutive bases introduced by Riquier (1893, 1899, 1910) and in Janet (1920, 1924, 1927) and we generalize the construction of Jmarked bases and termordering free reduction process introduced and deeply studied in Bertone et al. (2013a), Cioffi and Roggero (2011) for the special case of a strongly stable monomial ideal J. Here, we introduce and characterize for every monomial ideal J a particular complete set of generators F(J) , called stably complete, that allows an explicit description of the family Mf(J) . We obtain stronger results if J is quasistable, proving that F(J) is a Pommaret basis and Mf(J) has a natural structure of affine scheme. The final section presents a detailed analysis of the origin and the historical evolution of the main notions we refer to.  Keywords  Involutive bases, Quasistable ideals  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S074771711400073X 
Language  English  Journal  Journal of Symbolic Computation  Volume  68, Part 2  Number  0  Pages  87  108  Year  2015  Note  Effective Methods in Algebraic Geometry  Edition  0  Translation 
No  Refereed 
No 
