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Title: | Some Remarks on Homogeneous Minimal Reductions | Authors: | Spangher, Walter | Keywords: | Homogeneous Minimal Reduction; Quasi Complete Intersection; Scheme- Theoretic Generation; Monomial 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. |
Type: | Article | URI: | http://hdl.handle.net/10077/4188 | 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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SpangherRendMat39.pdf | 136.85 kB | Adobe PDF | ![]() View/Open |
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