Bipolynomial Hilbert functions
نویسندگان
چکیده
منابع مشابه
SYZYGIES and HILBERT FUNCTIONS
Throughout k stands for a field. For simplicity, we assume that k is algebraically closed and has characteristic 0. However, many of the open problems and conjectures make sense without these assumptions. The polynomial ring S = k[x1, . . . , xn] is graded by deg(xi) = 1 for all i. A polynomial f is homogeneous if f ∈ Si for some i, that is, if all monomial terms of f have the same degree. An i...
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This thesis is constituted of two articles, both related to Hilbert functions and h-vectors. In the first paper, we deal with h-vectors of reduced zero-dimensional schemes in the projective plane, and, in particular, with the problem of finding the possible h-vectors for the union of two sets of points of given h-vectors. In the second paper, we generalize the Green’s Hyperplane Restriction The...
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We study the closed convex hull of various collections of Hilbert functions. Working over a standard graded polynomial ring with modules that are generated in degree zero, we describe the supporting hyperplanes and extreme rays for the cones generated by the Hilbert functions of all modules, all modules with bounded a-invariant, and all modules with bounded Castelnuovo–Mumford regularity. The f...
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Let M be a finite module and let I be an arbitrary ideal over a Noetherian local ring. We define the generalized Hilbert function of I on M using the 0th local cohomology functor. We show that our definition re-conciliates with that of Ciupercă. By generalizing Singh’s formula (which holds in the case of λ(M/IM)<∞), we prove that the generalized Hilbert coefficients j0, . . . , jd−2 are preserv...
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For a standard graded algebra R, we consider embeddings of the poset of Hilbert functions of R-ideals into the poset of R-ideals, as a way of classification of Hilbert functions. There are examples of rings for which such embeddings do not exist. We describe how the embedding can be lifted to certain ring extensions, which is then used in the case of polarization and distraction. A version of a...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2010
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.04.008