2021/08/17 by Cooper, Susan M., Khoury, Sabine El, Faridi, Sara +4
#05E40 #13A15 #13D02 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2108.07703
This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers of a monomial ideal. We provide a full answer in the case of square-free monomial ideals of projective dimension one, by introducing a combinatorial construction of a family of (cubical) cell complexes whose 1-skeletons are powers of a graph that supports the resolution of the ideal.