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arXiv · 1502.06762

On the Hilbert series of ideals generated by generic forms

Lisa Nicklasson
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Abstract

There is a longstanding conjecture by Fr\"oberg about the Hilbert series of the ring $R/I$, where $R$ is a polynomial ring, and $I$ an ideal generated by generic forms. We prove this conjecture true in the case when $I$ is generated by a large number of forms, all of the same degree. We also conjecture that an ideal generated by $m$'th powers of forms of degree $d$ gives the same Hilbert series as an ideal generated by generic forms of degree $md$. We verify this in several cases. This also gives a proof of the first conjecture in some new cases.

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Lisa Nicklasson. 2015-02-24. On the Hilbert series of ideals generated by generic forms. https://doi.org/10.1080/00927872.2016.1236931

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