Stanley depth and symbolic powers of monomial ideals

• S. A. Seyed Fakhari ^[1]
  1. [1] University of Theran-IRAN
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 120, Nº 1, 2017, págs. 5-16
• Idioma: inglés
• DOI: 10.7146/math.scand.a-25501
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• Resumen

  • The aim of this paper is to study the Stanley depth of symbolic powers of a squarefree monomial ideal. We prove that for every squarefree monomial ideal I and every pair of integers k,s≥1, the inequalities sdepth(S/I(ks))≤sdepth(S/I(s)) and sdepth(I(ks))≤sdepth(I(s)) hold. If moreover I is unmixed of height d, then we show that for every integer k≥1, sdepth(I(k+d))≤sdepth(I(k)) and sdepth(S/I(k+d))≤sdepth(S/I(k)). Finally, we consider the limit behavior of the Stanley depth of symbolic powers of a squarefree monomial ideal. We also introduce a method for comparing the Stanley depth of factors of monomial ideals.