Frontiers of Mathematics in China

, Volume 13, Issue 2, pp 277–286 | Cite as

Castelnuovo-Mumford regularity and projective dimension of a squarefree monomial ideal

Research Article


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 u1; u2;...; um: Let w be the smallest number t with the property that for all integers 1 6 i1 < i2 <... < i t 6 m such that \(lcm({u_{{i_1}}},{u_{{i_2}}},...,{u_{{i_t}}}) = lcm({u_1},{u_2},...,{u_m})\) 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.


Castelnuovo-Mumford regularity projective dimension squarefree monomial ideals 


13F55 13C10 13C15 


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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.


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© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsSoochow UniversitySuzhouChina

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