منابع مشابه
Castelnuovo-Mumford regularity of seminormal simplicial affine semigroup rings
We show that the Eisenbud-Goto conjecture holds for seminormal simplicial affine semigroup rings. Moreover we prove an upper bound for the Castelnuovo-Mumford regularity in terms of the dimension, which is similar as in the normal case. Finally we compute explicitly the regularity of full Veronese rings.
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The face ring of a simplicial complex modulo m generic linear forms is shown to have finite local cohomology if and only if the link of every face of dimension m or more is nonsingular, i.e., has the homology of a wedge of spheres of the expected dimension. This is derived from an enumerative result for local cohomology of face rings modulo generic linear forms, as compared with local cohomolog...
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In this paper, we provide a simple proof for the fact that two simplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet rings are isomorphic as K-algebras. As a consequence, we show that two graphs are isomorphic if and only if their associated edge rings are isomorphic as K-algebras. Based on an explicit K-algebra isomorphism of two S...
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We will give a pure combinatorial proof of the Eisenbud-Goto conjecture for arbitrary monomial curves. In addition to this, we show that the conjecture holds for certain simplicial affine semigroup rings.
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A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1997
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(97)00051-0