Some Homological Properties of Borel Type Ideals

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Date
2022-02-01MFO Scientific Program
OWRF 2021Series
Oberwolfach Preprints;2022-03Author
Herzog, Jürgen
Moradi, Somayeh
Rahimbeigi, Masoomeh
Zhu, Guangjun
Metadata
Show full item recordOWP-2022-03
Abstract
We study ideals of Borel type, including $k$-Borel ideals and $t$-spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated squarefree principal Borel ideals are computed. For the multiplicity, the result is given under an additional assumption which is always satisfied for squarefree principal Borel ideals. These results are used to analyze the behaviour of height, multiplicity and analytic spread of the homological shift ideals $HS_j(I)$ as functions of $j$, when $I$ is an equigenerated squarefree
Borel ideal.