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Paper   IPM / M / 16042
School of Mathematics
  Title:   The absolutely Koszul and Backelin-Roos properties for spaces of quadrics of small codimension
  Author(s):  Rasoul Ahangari Maleki (Joint with L. M. Sega)
  Status:   Published
  Journal: J. Algebra
  Vol.:  551
  Year:  2020
  Pages:   232-284
  Supported by:  IPM
Let k be a field and let R be a quadratic standard graded k-algebra with dim R_2<4. We construct a graded surjective Golod homomorphism from 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.

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