Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE MINIMAL GRADED FREE RESOLUTION OF POWERS OF LEXSEGMENT IDEALS

  • Olteanu, Anda (Faculty of Mathematics and Computer Science Ovidius University)
  • Received : 2012.06.19
  • Published : 2013.05.01
Download PDF
⟨ Previous Next ⟩

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

References

  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. https://doi.org/10.4310/HHA.2002.v4.n2.a13
  8. H. Hulett and H. M. Martin, Betti numbers of lex-segment ideals, J. Algebra 275 (2004), no. 2, 629-638. https://doi.org/10.1016/S0021-8693(03)00383-1
  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.