Linear free resolutions and minimal multiplicity
نویسندگان
چکیده
منابع مشابه
Linear Free Resolutions and Minimal Multiplicity
Let S = k[x, ,..., x,] be a polynomial ring over a field and let A4 = @,*-a, M, be a finitely generated graded module; in the most interesting case A4 is an ideal of S. For a given natural number p, there is a great interest in the question: Can M be generated by (homogeneous) elements of degree <p? No simple answer, say in terms of the local cohomology of M, is known; but somewhat surprisingly...
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One of the most important computations in algebraic geometry or commutative algebra that a computer algebra system should provide is the computation of finite free resolutions of ideals and modules. Resolutions are used as an aid to understand the subtle nature of modules and are also a basis of further computations, such as computing sheaf cohomology, local cohomology, Ext, Tor, etc. Modern me...
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We begin the chapter with some history of the results that form the background of this book. We then define higher matrix factorizations, our main focus. While classical matrix factorizations were factorizations of a single element, higher matrix factorizations deal directly with sequences of elements. In section 1.3, we outline our main results. Throughout the book, we use the notation introdu...
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Let S = K[x1, . . . ,xn] be a polynomial ring and R = S/I where I ⊂ S is a graded ideal. The Multiplicity Conjecture of Herzog, Huneke, and Srinivasan states that the multiplicity of R is bounded above by a function of the maximal shifts in the minimal graded free resolution of R over S as well as bounded below by a function of the minimal shifts if R is Cohen–Macaulay. In this paper we study t...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1984
ISSN: 0021-8693
DOI: 10.1016/0021-8693(84)90092-9