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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)
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.
Type: Article
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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