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Title: Some Remarks on Homogeneous Minimal Reductions
Authors: Spangher, Walter
Keywords: Homogeneous Minimal ReductionQuasi Complete IntersectionScheme- Theoretic GenerationMonomial Varieties
Issue Date: 2007
Publisher: EUT Edizioni Università di Trieste
Source: Walter Spangher, "Some Remarks on Homogeneous Minimal Reductions”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 39 (2007), pp. 311–323.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (2007)
Abstract: Let I be a homogeneous ideal of a graded affine k–algebra R such that there exists some homogeneous minimal reduction. We prove that the degrees (of a basis) of every homogeneous minimal reduction J of I are uniquely determined by I; moreover if the fiber cone F(I) is reduced, then the last degree of J is equal to the last degree of I. Moreover, if R is Cohen– Macaulay and I is of analytic deviation one, with 0 < ht(I) := g, it is shown that the first g degrees of J are equals to the first g degrees of I. These results are applied to the ideals I of $k[x_0, . . . , x_{d−1}]$, which have scheme–th. generations of length \leq ht(I) + 2. Some examples are given.
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.39 (2007)

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