2021/06/29 by Keller VandeBogert, VandeBogert, Keller
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2106.15651
openalex publication_date 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A restricted dth power of an ideal I is obtained by restricting the exponent vectors allowed to appear on the "natural" generating set of Id, for some integer d. In this paper, we study homological properties of restricted powers of complete intersections. We construct an explicit minimal free resolution for any restricted power of a complete intersection which generalizes the L-complex construction of Buchsbaum and Eisenbud. We use this resolution to compute an explicit basis for the Koszul homology which allows us to deduce that the quotient defined by any restricted dth power of a complete intersection is a Golod ring for d ≥ 2. Finally, using techniques of Miller and Rahmati, we show that the minimal free resolution of the quotient defined by any restricted power of a complete intersection admits the structure of an associative DG-algebra.