Abstract
A Gotzmann monomial ideal of a polynomial ring is a monomial ideal which is generated in one degree and which satisfies Gotzmann's persistence theorem. Let R = K[x1,...,xn] denote the polynomial ring in n variables over a field K and Md the set of monomials of R of degree d. A subset V ⊂ Md is said to be a Gotzmann subset if the ideal generated by V is a Gotzmann monomial ideal. In the present paper, we find all integers a > 0 such that every Gotzmann subset V ⊂ Md with |V| = a is lexsegment (up to the permutations of the variables). In addition, we classify all Gotzmann subsets of K[x1, x2, x3].
| Original language | English |
|---|---|
| Pages (from-to) | 843-852 |
| Number of pages | 10 |
| Journal | Illinois Journal of Mathematics |
| Volume | 51 |
| Issue number | 3 |
| Publication status | Published - 2007 Sep 1 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Gotzmann monomial ideals. / Murai, Satoshi.
In: Illinois Journal of Mathematics, Vol. 51, No. 3, 01.09.2007, p. 843-852.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Gotzmann monomial ideals
AU - Murai, Satoshi
PY - 2007/9/1
Y1 - 2007/9/1
N2 - A Gotzmann monomial ideal of a polynomial ring is a monomial ideal which is generated in one degree and which satisfies Gotzmann's persistence theorem. Let R = K[x1,...,xn] denote the polynomial ring in n variables over a field K and Md the set of monomials of R of degree d. A subset V ⊂ Md is said to be a Gotzmann subset if the ideal generated by V is a Gotzmann monomial ideal. In the present paper, we find all integers a > 0 such that every Gotzmann subset V ⊂ Md with |V| = a is lexsegment (up to the permutations of the variables). In addition, we classify all Gotzmann subsets of K[x1, x2, x3].
AB - A Gotzmann monomial ideal of a polynomial ring is a monomial ideal which is generated in one degree and which satisfies Gotzmann's persistence theorem. Let R = K[x1,...,xn] denote the polynomial ring in n variables over a field K and Md the set of monomials of R of degree d. A subset V ⊂ Md is said to be a Gotzmann subset if the ideal generated by V is a Gotzmann monomial ideal. In the present paper, we find all integers a > 0 such that every Gotzmann subset V ⊂ Md with |V| = a is lexsegment (up to the permutations of the variables). In addition, we classify all Gotzmann subsets of K[x1, x2, x3].
UR - http://www.scopus.com/inward/record.url?scp=46849105869&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=46849105869&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:46849105869
VL - 51
SP - 843
EP - 852
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
SN - 0019-2082
IS - 3
ER -