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<p>The main goal of this paper is to obtain the upper bounds for the regularity of graded deficiency modules in the spirit of the one obtained by Kummini–Murai in the monomial case building upon the spectral sequence formalism developed by Àlvarez Montaner, Boix and Zarzuela. This spectral sequence formalism allows us not only to recover Kummini–Murai’s upper bound for monomial ideals, but also to extend it for other types of rings, which include toric face rings and some binomial edge rings, producing to the best of our knowledge new upper bounds for the regularity of graded deficiency modules of this type of rings.</p>

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Regularity of Deficiency Modules Through Spectral Sequences

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • Alberto F. Boix,
  • Santiago Zarzuela

摘要

The main goal of this paper is to obtain the upper bounds for the regularity of graded deficiency modules in the spirit of the one obtained by Kummini–Murai in the monomial case building upon the spectral sequence formalism developed by Àlvarez Montaner, Boix and Zarzuela. This spectral sequence formalism allows us not only to recover Kummini–Murai’s upper bound for monomial ideals, but also to extend it for other types of rings, which include toric face rings and some binomial edge rings, producing to the best of our knowledge new upper bounds for the regularity of graded deficiency modules of this type of rings.