On stability properties of powers of polymatroidal ideals

• Autores: Shokoufe Karimi, Amir Mafi
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 3, 2019, págs. 357-365
• Idioma: inglés
• DOI: 10.1007/s13348-018-0234-x
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let ?=?[?1,…,??] be the polynomial ring in n variables over a field K with the maximal ideal ?=(?1,…,??) . Let astab(?) and dstab(?) be the smallest integer n for which Ass(??) and depth(??) stabilize, respectively. In this paper we show that astab(?)=dstab(?) in the following cases:

    (i) I is a matroidal ideal and ?≤5 .

    (ii) I is a polymatroidal ideal, ?=4 and ?∉Ass∞(?) , where Ass∞(?) is the stable set of associated prime ideals of I.

    (iii) I is a polymatroidal ideal of degree 2.

    Moreover, we give an example of a polymatroidal ideal for which astab(?)≠dstab(?) . This is a counterexample to the conjecture of Herzog and Qureshi, according to which these two numbers are the same for polymatroidal ideals.