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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
CoCoA
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##### References:
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