[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2013.50.3.543

ON THE MINIMAL GRADED FREE RESOLUTION OF POWERS OF LEXSEGMENT IDEALS

Olteanu, Anda (Faculty of Mathematics and Computer Science Ovidius University)

Publication Information

Journal of the Korean Mathematical Society / v.50, no.3, 2013 , pp. 543-555 More about this Journal

Abstract

We consider powers of lexsegment ideals with a linear resolution (equivalently, with linear quotients) which are not completely lexsegment ideals. We give a complete description of their minimal graded free resolution.

Keywords

lexsegment ideals; linear resolution; linear quotients; monomial ideal;

Citations & Related Records

Reference

1	A. Aramova, E. De Negri, and J. Herzog, Lexsegment ideals with linear resolutions, Illinois J. Math. 42 (1998), no. 3, 509-523.
2	A. Conca, Regularity jumps for powers of ideals, Proceedings Lisbon Conference on Commutative Algebra, Lisbon-Portugal, 2003.
3	A. Conca and J. Herzog, Castelnuovo-Mumford regularity of products of ideals, Collect. Math. 54 (2003), no. 2, 137-152.
4	E. De Negri and J. Herzog, Completely lexsegment ideals, Proc. Amer. Math. Soc. 126 (1998), no. 12, 3467-3473.
5	V. Ene, A. Olteanu, and L. Sorrenti, Properties of lexsegment ideals, Osaka J. Math. 47 (2010), no. 1, 67-87.
6	V. Ene and A. Olteanu, Powers of lexsegment ideals with linear resolutions, arXiv:1011.2157, to appear in Illinois J. Math.
7	J. Herzog and Y. Takayama, Resolutions by mapping cones, Homology Homotopy Appl. 4 (2002), no. 2, 277-294. DOI
8	H. Hulett and H. M. Martin, Betti numbers of lex-segment ideals, J. Algebra 275 (2004), no. 2, 629-638. DOI ScienceOn
9	M. Ishaq, Lexsegment ideals are sequentially Cohen-Macaulay, ArXiv:1010.5615v2.
10	A. Olteanu, Normally torsion-free lexsegment ideals, arXiv: 1010.1473v1, to appear in Alg. Coll.
11	A. Olteanu, O. Olteanu, and L. Sorrenti, Gotzmann lexsegment ideals, Matematiche (Catania) 63 (2008), no. 2, 229-241.