Generic Subideals of Graph Ideals and Free Resolutions
نویسندگان
چکیده
منابع مشابه
Generic Subideals of Graph Ideals and Free Resolutions
For a graph of an n-cycle ∆ with Alexander dual ∆, we study the free resolution of a subideal G(n) of the Stanley-Reisner ideal I∆∗ . We prove that if G(n) is generated by 3 generic elements of I∆∗ , then the second syzygy module of G(n) is isomorphic to the second syzygy module of (x1, x2, . . . , xn). A result of Bruns shows that there is always a 3-generated ideal with this property. We show...
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Beginning with Hilbert’s construction of what is now called the Koszul complex [18], the study of finite free resolutions of modules over commutative rings has always proceeded by a study of certain particular generic resolutions. This has led to information about the structure of all finite free resolutions, as in [5] and [II], and to theorems on the structure and deformation of certain classe...
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It is interesting to ask how the invariants of the maps i, such as the ideal Ij(bi) generated by the j x j minors of q, reflect the properties of M. For example, it is not hard to show (see Buchsbaum-Eisenbud [4]) that if the grade of M is g (that is, g is the length of a maximal regular sequence contained in J) and r is the rank of the map b (that is, the size of the largest nonvanishing minor...
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Let X be an m × n matrix of indeterminates, m ≤ n, and T a new indeterminate. Consider the polynomial rings R0 = K[X] and R = R0[T ]. For a given positive integer t ≤ m, consider the ideal It = It(X) generated by the t-minors (i. e. the determinants of the t× t submatrices) of X . Using all these determinantal ideals, we define a new ideal J in R = R0[T ], which we call the generic graph constr...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2007
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181068762