On a conjecture of Vasconcelos via Sylvester forms. (November 2016)

• Record Type: Journal Article
• Authors: Burity, Ricardo; Simis, Aron; Tohǎneanu, Stefan O.
• Is Part Of: Journal of symbolic computation. Volume 77(2016)
• Page Start: 39
• Page End: 62
• Publication Date: 2016-11
• Subjects: 13A30 -- 13C14 -- 13D02 -- 13P10 -- 14E07 -- 14M07; Rees algebra -- Sylvester forms -- Almost Cohen–Macaulay -- Reduction number -- Monomials -- Initial ideal; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.01.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We study the structure of the Rees algebra of an almost complete intersection monomial ideal of finite co-length in a polynomial ring over a field, assuming that the least pure powers of the variables contained in the ideal have the same degree and that the additional monomial has the property that all variables have the same degree. It is shown that the Rees algebra has a natural quasi-homogeneous structure and its presentation ideal is generated by explicit Sylvester forms. A consequence of these results is a proof that the Rees algebra is almost Cohen–Macaulay, thus providing an affirmative partial answer to a conjecture of W. Vasconcelos.