Blowup algebras of determinantal ideals in prime characteristic
Abstract
We study when blowup algebras are -split or strongly -regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a symmetric matrix, and a Hankel matrix. We also study ideals of Pfaffians of a skew-symmetric matrix. We use these results to obtain bounds on the degrees of the defining equations for these algebras. We also prove that the limit of the normalized regularity of the symbolic powers of these ideals exists and that their depth stabilizes. Finally, we show that, for determinantal ideals, there exists a monomial order for which taking initial ideals commutes with taking symbolic powers. To obtain these results we develop the notion of -split filtrations and symbolic -split ideals.
Keywords
Cite
@article{arxiv.2109.00592,
title = {Blowup algebras of determinantal ideals in prime characteristic},
author = {Alessandro De Stefani and Jonathan Montaño and Luis Núñez-Betancourt},
journal= {arXiv preprint arXiv:2109.00592},
year = {2024}
}
Comments
Final version. This preprint corrects, replaces, and expands the work done in preprint arXiv:2004.03831, which contains a mistake Lemma 5.4. The new version changes some terminology. We also added a new result about F-regularity for symbolic Rees algebras of ideals associated to symmetric matrices (Theorem 6.16)