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arXiv · 1808.01822

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

Sabine El Khoury
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Abstract

Let $S$ be a polynomial ring over an algebraic closed field $k$ and $ \mathfrak p =(x,y,z,w) $ a homogeneous height four prime ideal. We give a finite characterization of the degree two 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 $e \leq 3$.

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Sabine El Khoury. 2018-08-06. On the projective dimension of $5$ quadric almost complete intersections with low multiplicities. https://arxiv.org/abs/1808.01822

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