## Rocky Mountain Journal of Mathematics

### On the projective dimension of $5$ quadric almost complete intersections with low multiplicities

Sabine El Khoury

#### Abstract

Let $S$ be a polynomial ring over an algebraically closed field $k$ and $\mathfrak p =(x,y,z,w)$ a homogeneous height $4$ prime ideal. We give a finite characterization of the degree $2$ component of ideals primary to $\mathfrak p$, with multiplicity $e \leq 3$. We use this result to give a tight bound on the projective dimension of almost complete intersections generated by five quadrics with $e \leq 3$.

#### Article information

Source
Rocky Mountain J. Math., Volume 49, Number 5 (2019), 1491-1546.

Dates
First available in Project Euclid: 19 September 2019

https://projecteuclid.org/euclid.rmjm/1568880089

Digital Object Identifier
doi:10.1216/RMJ-2019-49-5-1491

Mathematical Reviews number (MathSciNet)
MR4010571

Zentralblatt MATH identifier
07113697

Subjects
Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13D05: Homological dimension

#### Citation

Khoury, Sabine El. On the projective dimension of $5$ quadric almost complete intersections with low multiplicities. Rocky Mountain J. Math. 49 (2019), no. 5, 1491--1546. doi:10.1216/RMJ-2019-49-5-1491. https://projecteuclid.org/euclid.rmjm/1568880089

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