TY - JOUR
T1 - Free resolutions of lex-ideals over a koszul toric ring
AU - Murai, Satoshi
PY - 2011/2
Y1 - 2011/2
N2 - In this paper, we study the minimal free resolution of lex-ideals over a Koszul toric ring. In particular, we study in which toric ring R all lexidealsare componentwise linear. We give a certain necessity and sufficiency condition for this property, and show that lex-ideals in a strongly Koszul toric ring are componentwise linear. In addition, it is shown that, in the toric ring arising from the Segre product 1 × ⋯ ×1, every Hilbert function of a graded ideal is attained by a lex-ideal and that lex-ideals have the greatest graded Betti numbers among all ideals having the same Hilbert function.
AB - In this paper, we study the minimal free resolution of lex-ideals over a Koszul toric ring. In particular, we study in which toric ring R all lexidealsare componentwise linear. We give a certain necessity and sufficiency condition for this property, and show that lex-ideals in a strongly Koszul toric ring are componentwise linear. In addition, it is shown that, in the toric ring arising from the Segre product 1 × ⋯ ×1, every Hilbert function of a graded ideal is attained by a lex-ideal and that lex-ideals have the greatest graded Betti numbers among all ideals having the same Hilbert function.
KW - Componentwise linear ideals
KW - Free resolutions
KW - Hilbert functions
KW - Koszul algebras
KW - Lex-ideals
KW - Toric rings
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U2 - 10.1090/S0002-9947-2010-05074-3
DO - 10.1090/S0002-9947-2010-05074-3
M3 - Article
AN - SCOPUS:78651315887
SN - 0002-9947
VL - 363
SP - 857
EP - 885
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -