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arXiv · 1801.08195

The projective dimension of three cubics is at most 5

Paolo Mantero·Jason McCullough
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Abstract

Let $R$ be a polynomial ring over a field and $I$ an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension $\mathrm{pd}(R/I)$ of $R/I$ is at most 36, although the example with largest projective dimension he constructed has $\mathrm{pd}(R/I)=5$. Based on computational evidence, it had been conjectured that $\mathrm{pd}(R/I)\leq 5$. In the present paper we prove this conjectured sharp bound.

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Paolo Mantero, Jason McCullough. 2018-01-24. The projective dimension of three cubics is at most 5. https://arxiv.org/abs/1801.08195

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