Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896497 | Journal of Algebra | 2018 | 14 Pages |
Abstract
Given an ideal I=(f1,â¦,fr) in C[x1,â¦,xn] generated by forms of degree d, and an integer k>1, how large can the ideal Ik be, i.e., how small can the Hilbert function of C[x1,â¦,xn]/Ik be? If râ¤n the smallest Hilbert function is achieved by any complete intersection, but for r>n, the question is in general very hard to answer. We study the problem for r=n+1, where the result is known for k=1. We also study a closely related problem, the Weak Lefschetz property, for S/Ik, where I is the ideal generated by the d'th powers of the variables.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Mats Boij, Ralf Fröberg, Samuel Lundqvist,