Radical generic initial ideals
Commutative Algebra
2021-08-24 v1
Abstract
In this paper, we survey the theory of Cartwright-Sturmfels ideals. These are Z^n-graded ideals, whose multigraded generic initial ideal is radical. Cartwright-Sturmfels ideals have surprising properties, mostly stemming from the fact that their Hilbert scheme only contains one Borel-fixed point. This has consequences, e.g., on their universal Groebner bases and on the family of their initial ideals. In this paper, we discuss several known classes of Cartwright-Sturmfels ideals and we find a new one. Among determinantal ideals of same-size minors of a matrix of variables and Schubert determinantal ideals, we are able to characterize those that are Cartwright-Sturmfels.
Cite
@article{arxiv.2108.10115,
title = {Radical generic initial ideals},
author = {A. Conca and E. De Negri and E. Gorla},
journal= {arXiv preprint arXiv:2108.10115},
year = {2021}
}