A sharp bound for the Castelnuovo–Mumford regularity of subspace arrangements
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چکیده
منابع مشابه
A Sharp Bound for the Castelnuovo-mumford Regularity of Subspace Arrangements Harm Derksen and Jessica Sidman
Over the past twenty years rapid advances in computational algebraic geometry have generated increasing amounts of interest in quantifying the “complexity” of ideals and modules. For a finitely generated module M over a polynomial ring S = k[x0, . . . , xn] with k an arbitrary field, we say that M is r-regular (in the sense of Castelnuovo and Mumford) if the i-th syzygy module of M is generated...
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We study bounds for the Castelnuovo–Mumford regularity of homogeneous ideals in a polynomial ring in terms of the number of variables and the degree of the generators. In particular, our aim is to give a positive answer to a question posed by Bayer and Mumford in What can be computed in algebraic geometry? (Computational algebraic geometry and commutative algebra, Symposia Mathematica, vol. XXX...
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A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$, denoted by match$(G)$. In this paper, we provide a generalization of this result for powers of edge ideals. More precisely, we show that for every graph $G$ and every $sgeq 1$, $${rm reg}( R/ I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...
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New inequalities for subspace arrangements
For each positive integer n ≥ 4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n = 4 we recover Ingleton’s inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2002
ISSN: 0001-8708
DOI: 10.1016/s0001-8708(02)00019-1