TY - JOUR
T1 - Borel-plus-powers monomial ideals
AU - Murai, Satoshi
N1 - Funding Information:
The author is supported by the JSPS Research Fellowships for Young Scientists.
PY - 2008/6
Y1 - 2008/6
N2 - Let S = K [x1, ..., xn] be a standard graded polynomial ring over a field K. In this paper, we show that the lex-plus-powers ideal has the largest graded Betti numbers among all Borel-plus-powers monomial ideals with the same Hilbert function. In addition in the case of characteristic 0, by using this result, we prove the lex-plus-powers conjecture for graded ideals containing x1p, ..., xnp, where p is a prime number.
AB - Let S = K [x1, ..., xn] be a standard graded polynomial ring over a field K. In this paper, we show that the lex-plus-powers ideal has the largest graded Betti numbers among all Borel-plus-powers monomial ideals with the same Hilbert function. In addition in the case of characteristic 0, by using this result, we prove the lex-plus-powers conjecture for graded ideals containing x1p, ..., xnp, where p is a prime number.
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U2 - 10.1016/j.jpaa.2007.09.010
DO - 10.1016/j.jpaa.2007.09.010
M3 - Article
AN - SCOPUS:38849117611
SN - 0022-4049
VL - 212
SP - 1321
EP - 1336
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 6
ER -