Gin and Lex of certain monomial ideals

Details Gin and Lex of certain monomial ideals Gin and Lex of certain monomial ideals

2005-09-18

arxiv.org/abs/math/0509403v2

Math. Scand. 99 (2006), no. 1, 76--86

Mathematics

Commutative Algebra

9 pages, minor grammatical changes

Scientific paper

Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$ of characteristic 0 with each $\deg x_i = 1$. Given arbitrary integers $i$ and $j$ with $2 \leq i \leq n$ and $3 \leq j \leq n$, we will construct a monomial ideal $I \subset A$ such that (i) $\beta_k(I) < \beta_k(\Gin(I))$ for all $k < i$, (ii) $\beta_i(I) = \beta_i(\Gin(I))$, (iii) $\beta_\ell(\Gin(I)) < \beta_\ell(\Lex(I))$ for all $\ell < j$ and (iv) $\beta_j(\Gin(I)) = \beta_j(\Lex(I))$, where $\Gin(I)$ is the generic initial ideal of $I$ with respect to the reverse lexicographic order induced by $x_1 > >... > x_n$ and where $\Lex(I)$ is the lexsegment ideal with the same Hilbert function as $I$.

Affiliated with

Also associated with

No associations

Rating

Gin and Lex of certain monomial ideals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gin and Lex of certain monomial ideals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gin and Lex of certain monomial ideals will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-654284