标题： 通过谱序列的亏格模的正则性 显示英文标题

标题： Regularity of deficiency modules through spectral sequences

摘要： 本文的主要目标是在Kumini--Murai在单项式情况下的结果的精神下，通过Àlvarez Montaner、Boix和Zarzuela发展的谱序列形式化方法，获得分次缺陷模的正则性的上界。这种谱序列形式化不仅使我们能够恢复Kumini--Murai对单项式理想得到的上界，还能将其扩展到其他类型的环，这些环包括toric face环和一些二项式边环，在我们所知的范围内，为这类环的分次缺陷模的正则性提供了新的上界。 显示英文摘要

摘要： The main goal of this paper is to obtain upper bounds for the regularity of graded deficiency modules in the spirit of the one obtained by Kumini--Murai in the monomial case building upon the spectral sequence formalism developed by \`Alvarez Montaner, Boix and Zarzuela. This spectral sequence formalism allows us not only to recover Kumini--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.