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The absolutely Koszul and Backelin-Roos properties for spaces of quadrics of small codimension Sega, Liana


Let $k$ be a field and let $R$ be a quadratic standard graded $k$-algebra with $\dim_{k}R_2\le 3$. We construct a graded surjective Golod homomorphism $\varphi \colon P\to R$ such that $P$ is a complete intersection of codimension at most $3$. Furthermore, we show that $R$ is absolutely Koszul (that is, every finitely generated $R$-module has finite linearity defect) if and only if $R$ is Koszul if and only if $R$ is not a trivial fiber extension of a non-Koszul and non-Artinian quadratic algebra of embedding dimension $3$. In particular, we recover earlier results on the Koszul property of Backelin, Conca and D'Al\`i. This is joint work with R. Maleki.

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