2019/01/30 by Cioffi, Francesca
#11Y55 #13P99 #14Q99 #68W30 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1901.10974
Given the Hilbert function u of a closed subscheme of a projective space over an infinite field K, let mu and Mu be, respectively, the minimum and the maximum among all the Castelnuovo-Mumford regularities of schemes with Hilbert function u. I show that, for every integer m such that mu ≤ m ≤ Mu, there exists a scheme with Hilbert function u and Castelnuovo-Mumford regularity m. As a consequence, the analogous algebraic result for an O-sequence f and homogeneous polynomial ideals over K with Hilbert function f holds too. Although this result does not need any explicit computation, I also describe how to compute a scheme with the above requested properties. Precisely, I give a method to construct a strongly stable ideal defining such a scheme.