Ja n 20 01 GRÖBNER BASES AND REGULARITY OF REES ALGEBRAS
نویسندگان
چکیده
Introduction Let B = k[x 1 ,. .. , x n ] be a polynomial ring over a field k and A = B/J a quotient ring of B by a homogeneous ideal J. Let m denote the maximal graded ideal of A. Then the Rees algebra R = A[mt] may be considered a standard graded k-algebra and has a presentation B[y 1 ,. In this paper we want to compare the ideals J and I J as well as their homological properties.
منابع مشابه
THE REGULARITY OF TOR AND GRADED BETTI NUMBERS By DAVID EISENBUD, CRAIG HUNEKE and BERND ULRICH
Let S = K[x1, . . . , xn], let A, B be finitely generated graded S-modules, and let m = (x1, . . . , xn) ⊂ S. We give bounds for the regularity of the local cohomology of Tork (A, B) in terms of the graded Betti numbers of A and B, under the assumption that dim Tor1 (A, B) ≤ 1. We apply the results to syzygies, Gröbner bases, products and powers of ideals, and to the relationship of the Rees an...
متن کاملM ay 2 00 4 The Regularity of Tor and Graded
We give bounds for the regularity of the local cohomology of Tor k (A, B) in terms of the graded Betti numbers of A and B, under the assumption that dim Tor 1 (A, B) ≤ 1. We apply the results to syzygies, Gröbner bases, products and powers of ideals, and to the relationship of the Rees and Symmetric algebras. For example we show that any homogeneous linearly presented m-primary ideal has some p...
متن کاملDimension-Dependent Upper Bounds for Gröbner Bases
We improve certain degree bounds for Gröbner bases of polynomial ideals in generic position. We work exclusively in deterministically verifiable and achievable generic positions of a combinatorial nature, namely either strongly stable position or quasi stable position. Furthermore, we exhibit new dimension(and depth-)dependent upper bounds for the Castelnuovo-Mumford regularity and the degrees ...
متن کاملar X iv : m at h / 02 10 07 9 v 1 [ m at h . A C ] 4 O ct 2 00 2 GRÖBNER BASES , LOCAL COHOMOLOGY AND REDUCTION NUMBER
D. Bayer and M. Stillman showed that Gröbner bases can be used to compute the Castelnuovo-Mumford regularity which is a measure for the vanishing of graded local cohomology modules. The aim of this paper is to show that the same method can be applied to study other cohomological invariants as well as the reduction number.
متن کاملAnalysis of the MQQ Public Key Cryptosystem
MQQ is a multivariate cryptosystem based on multivariate quadratic quasigroups and the Dobbertin transformation [18]. The cryptosystem was broken both by Gröbner bases computation and MutantXL [27]. The complexity of Gröbner bases computation is exponential in the degree of regularity, which is the maximum degree of polynomials occurring during the computation. The authors of [27] observed that...
متن کامل