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Showing 1 to 13 of 13 for “"Cohen-Macaulay"”.
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Representation Theory of Orders over Cohen-Macaulay Rings
… an R-order is an R-algebra which is a maximal CohenMacaulay</p> <p>R-module. In this thesis we consider orders, Λ, over Cohen-Macaulay local rings</p> <p>R possessing a canonical module, ωR. In this case a great deal of structure is imposed on Λ.</p> <p>In Chapter 3 we focus on the use of …
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A compact moduli space for Cohen-Macaulay curves in projective space
… finite maps from a projective (locally) Cohen-Macaulay curve to a fixed projective space. The definition of the functor includes a number of technical conditions, but the most important is that the map is almost everywhere an isomorphism onto its image. The motivation for this definition …
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Four Generated Rank 2 Arithmetically Cohen-Macaulay Vector Bundles on General Sextic Surfaces
… generated indecomposable rank 2 arithmetically Cohen-Macaulay: ACM for short) bundles on a general sextic surface.</p><p>In Chapter One we introduce preliminaries and prove on a general sextic surface, every four generated indecomposable rank 2 ACM bundle belongs to one of fourteen cases. In …
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Some problems in polynomial interpolation and topological complexity
… related to simplicial complexes which are Cohen-Macaulay and have a Cohen-Macaulay dual. In Chapter 2, we will discuss the motion planning problem in complex hyperplane arrangement complements. The difficulty of constructing a minimally discontinuous motion planning algorithm for a …
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Double affine Hecke algebras and noncommutative geometry
… algebra H(t, 1) of type An-1 is an integral Cohen-Macaulay algebra isomorphic to the center Z of H(t, 1), and H(t, 1)e is a Cohen-Macaulay eH(t, 1)e-module with the property H(t, 1) = EndeH(t,tl)(H(t, 1)e). This implies the classification of the finite dimensional representations of the …
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Invariant polynomials and machine learning
… generators. Additionally, we use the Cohen-Macaulay structure of the Lorentz-invariant algebra to provide a more direct characterisation in terms of a Hironaka decomposition. Although such a characterisation would na\"ively not be expected for the Euclidean-invariant algebra (since the …
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Auslander-Reiten Sequences over Gorenstein Rings of Dimension One
… maximal ideal m. We show that if M is a maximal Cohen-Macaulay R-module which begins an Auslander-Reiten sequence, then this sequence is produced by an endomorphism of m, which we call a Frobenius element. We observe that Frobenius elements can be easier to identify when R is a graded ring, …
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The Behavior on the Restriction of Divisor Classes to Sequences of Hypersurfaces
… zero, dim A ≥ 4, and A has a small Cohen-Macaulay module, then we show that there is an integer N > 0 such that fn ∈ mN ⇒ jn* is injective. We substantiate these results with a general construction that provides a large collection of examples.
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Matrix Factorizations With More Than Two Factors
… hypersurface ring defined by $f+z^d$ has finite Cohen-Macaulay representation type.</p><p>In Chapter 5, we provide a generalization of Eisenbud's fundamental theorem on the connection between matrix factorizations of $f$ and maximal Cohen-Macaulay modules over the hypersurface ring defined by …
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The syzygy theorem and the weak Lefschetz Property
… p, with the case of syzygies of prime ideals of Cohen-Macaulay local rings of unramified mixed characteristic being noted. We reduce the remaining considerations to modules annihilated by p^s, s > 0, that have finite projective dimension over a hypersurface ring. Our main results are obtained as …
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Weak Purity for Gorenstein Rings
… numerous examples which show that A need not be Cohen-Macaulay, hence that the extension need not be unramified. In a related context, the main portion of the thesis addresses the purity of the extension $B\to A.$ The setting is as follows: $B\to A$ is a module finite extension of normal rings, …
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On quasi-dominant weights and Hilbert series of determinantal varieties.
… of invariant theory. Since these rings are Cohen-Macaulay, their Hilbert series are rational functions whose numerator polynomials have nonnegative integer coefficients. In the case of general determinantal varieties, as well as in the case of symmetric determinantal varieties, these …
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Components of the Emerton-Gee Moduli Stack of Galois Representations for GL2 and A Graph-Theoretic Approach to Computing Selmer Groups of Elliptic Curves over Q(i)
… of these components admit smooth–local covers by Cohen-Macaulay and resolution-rational varieties, which are generally not Gorenstein. Finally, we determine the singular loci in the components, providing insights which up- date expectations about the conjectural categorical p–adic Langlands …