Publication: Some Remarks on Homogeneous Minimal Reductions
Date
2007
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
EUT Edizioni Università di Trieste
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.
Description
Keywords
Homogeneous Minimal Reduction, Quasi Complete Intersection, Scheme- Theoretic Generation, Monomial Varieties
Citation
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.