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The range of all regularities for polynomial ideals with a given Hilbert function. (English) Zbl 07268500
Summary: Let \(A\) denote any polynomial ring over a field \(K\) and \(I\) any homogeneous ideal of \(A\). In this paper it is proven that, given an Hilbert function \(u\), the set of the regularities of the homogeneous ideals \(I\) such that the \(K\)-algebra \(A / I\) has Hilbert function \(u\) is an interval of integers. This result is achieved by means of constructive arguments related to the minimal functions with a given Hilbert polynomial and a given regularity.
MSC:
13P99 Computational aspects and applications of commutative rings
14Q99 Computational aspects in algebraic geometry
68W30 Symbolic computation and algebraic computation
11Y55 Calculation of integer sequences
Software:
CoCoA
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References:
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