Limits of saturated ideals
Commutative Algebra
2025-02-25 v3 Algebraic Geometry
Abstract
We investigate the question whether a given homogeneous ideal is a limit of saturated ones. We provide cohomological necessary criteria for this to hold and apply them to a range of examples. Our motivation comes from the theory of border apolarity and varieties of sums of powers, where the question above is tightly connected to proving new lower bounds for border ranks of tensors.
Keywords
Cite
@article{arxiv.2210.13579,
title = {Limits of saturated ideals},
author = {Joachim Jelisiejew and Tomasz Mańdziuk},
journal= {arXiv preprint arXiv:2210.13579},
year = {2025}
}
Comments
v3, minor corrections