Construction of almost revlex ideals with Hilbert function of some complete intersections. (arXiv:1803.02330v2 [math.AC] UPDATED)

We give a constructive proof of the existence of the almost revlex ideal $J\subset K[x_1,\dots,x_n]$ with the same Hilbert function of a complete intersection defined by $n$ forms of degrees $d_1\leq \dots \leq d_n$, when for every $i\geq 4$ the degrees satisfy the condition $d_i\geq \bar u_{i-1}+1=\min\Bigl\{\Big\lfloor\frac{\sum_{j=1}^{i-1}d_j-i+1}{2}\Big\rfloor, \sum_{j=1}^{i-2} d_j-i+2\Bigr\}+1$. The further property that, for every $t\geq \bar u_n+1$, all terms of degree $t$ outside $J$ are divisible by the last variable has an important role in our inductive and constructive proof, which is different from the more general construction given by Pardue in 2010. 查看全文>>