Symbolic Powers and Free Resolutions of Generalized Star Configurations of Hypersurfaces

As a generalization of the ideals of star configurations of hypersurfaces, we consider the $a$-fold product ideal $Ia(f1^{m1}\cdots fs^{ms})$ when ${f1,\dots,fs}$ is a sequence of $n$-generic forms and $1\le a\le m1+\cdots+ms$. Firstly, we show that this ideal has complete intersection quotients when these forms are of the same degree and essentially linear. Then we study its symbolic powers while focusing on the uniform case with $m1=\cdots=m_s$. For large $a$, we describe its resurgence and symbolic defect. And for general $a$, we also investigate the corresponding invariants for meeting-at-the-minimal-components version of symbolic powers.

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Work Title Symbolic Powers and Free Resolutions of Generalized Star Configurations of Hypersurfaces
Access
Open Access
Creators
  1. Kuei-Nuan Lin
  2. Yi-Huang Shen
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Michigan Math. J.
Publication Date July 23, 2021
Publisher Identifier (DOI)
  1. 10.1307/mmj/20205890
Deposited November 17, 2021

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