2019/12/05 by Kenkel, Jennifer
#13D45 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1912.02917
Let R be a standard graded polynomial ring that is finitely generated over a field of characteristic 0, let \mathfrakm be the homogeneous maximal ideal of R, and let I be a homogeneous prime ideal of R. Dao and Montaño defined an invariant that, in the case that Proj(R/I) is lci and for cohomological index less than dim(R/I), measures the asymptotic growth of lengths of local cohomology modules of thickenings. They showed its existence and rationality for certain classes of monomial ideals I. The following affirms that the invariant exists and is rational for rings R = ℂ[X] where X is a 2 × m matrix and I is the ideal generated by size two minors and is to our knowledge, the first non-monomial calculation of this invariant.