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Showing 1 to 8 of 8 for “"free resolutions"”.
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Free resolutions, combinatorics, and geometry
Boij-Söderberg theory is the study of two cones: the first is the cone of graded Betti tables over a polynomial ring, and the second is the cone of cohomology tables of coherent sheaves over projective space. Each cone has a triangulation induced from a certain partial order. Our first result gives …
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Simplicial posets--f-vectors and free resolutions
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1991.
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Ideals of powers of linear forms
… of Postnikov and Shapiro concerning the minimal free resolutions of a class of ideals of powers of linear forms in n variables which are constructed from complete graphs on n + 1 vertices. This statement was also conjectured by Schenck in the special case of n = 3. We provide two different …
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Betti numbers of Koszul algebras and codimension two matrix factorizations
… consists of two projects on the structure of free resolutions in commutative algebra. After developing some necessary background, we prove a structure theorem in Chapter 3 for the defining ideals of Koszul almost complete intersections and, in the process, give an affirmative answer for all …
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Homology over a Complete Intersection Ring via the Generic Hypersurface
… this approach is that over a hypersurface ring, free resolutions are eventually 2-periodic, given by matrix factorizations, and are thus relatively easy to understand. We approach this relationship in two ways. First, we give a correspondence between the two rings in the graded setting, where …
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Koszul Homology and Resolutions over Commutative Rings
… relationship between Koszul homology and minimal free resolutions in various settings. We provide tools which allow one to view Koszul homology in a concrete way, and use these tools in a number of applications.</p> <p>One setting in which we examine Koszul homology is provided by the notion of …
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Matrix Factorizations With More Than Two Factors
… introduced by Eisenbud in his study of free resolutions of modules over hypersurface rings. Many of the results given in this thesis are extensions of well-known results in the $d=2$ case while others give new and unexpected properties which only arise when $d>2$.</p><p>First we …
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A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices
… projective dimension over polynomial rings whose free resolutions have known special structure. We begin with projective modules and investigate a computational approach to a famous theorem of Quillen-Suslin, which states that every finitely generated projective module over S = R[x_1,...,x_n], …