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Some Remarks on Homogeneous Minimal Reductions
Spangher, Walter
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (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.
Languages
en
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