Let S = K[x1, x2,..., xn] be the polynomial ring in n variables over a field K, and let I be a squarefree monomial ideal minimally generated by the monomials ul,u2,...,Um. Let w be the smallest number t with the prope...Let S = K[x1, x2,..., xn] be the polynomial ring in n variables over a field K, and let I be a squarefree monomial ideal minimally generated by the monomials ul,u2,...,Um. Let w be the smallest number t with the property that for all integers 1 ≤ i1 〈 i2 〈 … 〈 it ≤ m such that lcm（uil, ui2,..., uii） = lcm（ul,u2,...,Um）. We give an upper bound for Castelnuovo-Mumford regularity of I by the bigsize of I. As a corollary, the projective dimension of I is bounded by the number w.展开更多
This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived...This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.展开更多
基金This work was supported in part by the National Natural Science Foundation of China （Grant No. 11201326）, the Natural Science Foundation of Jiangsu Province （No. BK2011276）, and the Jiangsu Provincial Training Programs of Innovation and Entrepreneurship for Undergraduates.
文摘Let S = K[x1, x2,..., xn] be the polynomial ring in n variables over a field K, and let I be a squarefree monomial ideal minimally generated by the monomials ul,u2,...,Um. Let w be the smallest number t with the property that for all integers 1 ≤ i1 〈 i2 〈 … 〈 it ≤ m such that lcm（uil, ui2,..., uii） = lcm（ul,u2,...,Um）. We give an upper bound for Castelnuovo-Mumford regularity of I by the bigsize of I. As a corollary, the projective dimension of I is bounded by the number w.
文摘This paper develops a duality theory for connected cochain DG algebras,with particular emphasis on the non-commutative aspects.One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology.As an application,it is proved that if the canonical module k=A/A≥1 has a semi-free resolution where the cohomological degree of the generators is bounded above,then the same is true for each DG module with finitely generated cohomology.
