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arXiv · 1612.01558

Koszul Algebras Defined by Three Relations

Adam Boocher·S. Hamid Hassanzadeh·Srikanth B. Iyengar
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Abstract

This work concerns commutative algebras of the form $R=Q/I$, where $Q$ is a standard graded polynomial ring and $I$ is a homogenous ideal in $Q$. It has been proposed that when $R$ is Koszul the $i$th Betti number of $R$ over $Q$ is at most $\binom gi$, where $g$ is the number of generators of $I$; in particular, the projective dimension of $R$ over $Q$ is at most $g$. The main result of this work settles this question, in the affirmative, when $g\le 3$.

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Adam Boocher, S. Hamid Hassanzadeh, Srikanth B. Iyengar. 2016-12-05. Koszul Algebras Defined by Three Relations. https://arxiv.org/abs/1612.01558

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