Castelnuovo-Mumford Regularity of Graphs
نویسندگان
چکیده
منابع مشابه
Multigraded Castelnuovo-mumford Regularity
We develop a multigraded variant of Castelnuovo-Mumford regularity. Motivated by toric geometry, we work with modules over a polynomial ring graded by a finitely generated abelian group. As in the standard graded case, our definition of multigraded regularity involves the vanishing of graded components of local cohomology. We establish the key properties of regularity: its connection with the m...
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The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given an approximation by modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the m...
متن کاملVertex-decomposable Graphs, Codismantlability, Cohen-Macaulayness, and Castelnuovo-Mumford Regularity
We call a vertex x of a graph G = (V,E) a codominated vertex if NG[y] ⊆ NG[x] for some vertex y ∈ V \{x}, and a graph G is called codismantlable if either it is an edgeless graph or it contains a codominated vertex x such that G − x is codismantlable. We show that (C4, C5)-free vertex-decomposable graphs are codismantlable, and prove that if G is a (C4, C5, C7)-free well-covered graph, then ver...
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This is not the case in general. There are examples already with M = I such that reg(I) > 2 reg(I), see Sturmfels [15] and Terai [16]. On the other hand, Chandler [5] and Geramita, Gimigliano and Pitteloud [11] have shown that reg(I) ≤ k reg(I) holds for ideals with dimR/I ≤ 1. In general one has that reg(I) is asymptotically a linear function of k, see [14, 8]. If one takes I = m and M any gra...
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Let I be a homogeneous ideal of the polynomial ring K[x0, . . . , xn], where K is an arbitrary field. Avoiding the construction of a minimal graded free resolution of I, we provide effective methods for computing the Castelnuovo-Mumford regularity of I that also compute other cohomological invariants of K[x0, . . . , xn]/I. We then apply our methods to the defining ideal I(V) of a projective mo...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2018
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-017-3450-1