Search: WFRF:(Altafi Nasrin)
> (2023) >
Number of generator...
Number of generators of ideals in Jordan cells of the family of graded Artinian algebras of height two
-
- Altafi, Nasrin (author)
- KTH,Matematik (Avd.)
-
- Iarrobino, Anthony (author)
- Department of Mathematics, Northeastern University, Boston, MA 02115, USA
-
- Khatami, Leila (author)
- Union College, Schenectady, New York, 12308, USA
-
show more...
-
- Yaméogo, Joachim (author)
- Université Côte d'Azur, CNRS, LJAD, France
-
show less...
-
KTH Matematik (Avd) (creator_code:org_t)
- Elsevier BV, 2023
- 2023
- English.
-
In: Journal of Pure and Applied Algebra. - : Elsevier BV. - 0022-4049 .- 1873-1376. ; 227:12
- Related links:
-
https://doi.org/10.1...
-
show more...
-
https://urn.kb.se/re...
-
https://doi.org/10.1...
-
show less...
Abstract
Subject headings
Close
- We let A=R/I be a standard graded Artinian algebra quotient of R=k[x,y], the polynomial ring in two variables over a field k by an ideal I, and let n be its vector space dimension. The Jordan type Pℓ of a linear form ℓ∈A1 is the partition of n determining the Jordan block decomposition of the multiplication on A by ℓ – which is nilpotent. The first three authors previously determined which partitions of n=dimkA may occur as the Jordan type for some linear form ℓ on a graded complete intersection Artinian quotient A=R/(f,g) of R, and they counted the number of such partitions for each complete intersection Hilbert function T [1]. We here consider the family GT of graded Artinian quotients A=R/I of R=k[x,y], having arbitrary Hilbert function H(A)=T. The Jordan cell V(EP) corresponding to a partition P having diagonal lengths T is comprised of all ideals I in R whose initial ideal is the monomial ideal EP determined by P. These cells give a decomposition of the variety GT into affine spaces. We determine the generic number κ(P) of generators for the ideals in each cell V(EP), generalizing a result of [1]. In particular, we determine those partitions for which κ(P)=κ(T), the generic number of generators for an ideal defining an algebra A in GT. We also count the number of partitions P of diagonal lengths T having a given κ(P). A main tool is a combinatorial and geometric result allowing us to split T and any partition P of diagonal lengths T into simpler Ti and partitions Pi, such that V(EP) is the product of the cells V(EPi), and Ti is single-block: GTi is a Grassmannian.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Artinian algebra
- Cellular decomposition
- Hilbert function
- Hook code
- Jordan type
- Partition
Publication and Content Type
- ref (subject category)
- art (subject category)
Find in a library
To the university's database