Term-ordering free involutive bases

摘要: In this paper, we consider a monomial ideal J ? P : = A x 1 , n over commutative ring A, and face the problem of characterization for family M f ( ) all homogeneous ideals I such that A-module / is free with basis given by set terms in Grobner escalier N J. This general wider than having as initial w.r.t. any term-ordering, hence more suited to computational approach study Hilbert schemes.For purpose, exploit enhance concepts multiplicative variables, complete sets involutive bases introduced Riquier (1893, 1899, 1910) Janet (1920, 1924, 1927) generalize construction J-marked term-ordering reduction process deeply studied Bertone et al. (2013a), Cioffi Roggero (2011) special case strongly stable J.Here, introduce characterize every particular generators F called stably complete, allows an explicit description . We obtain stronger results if quasi-stable, proving Pommaret has natural structure affine scheme.The final section presents detailed analysis origin historical evolution main notions refer to.