Blowup algebras of determinantal ideals in prime characteristic
Abstract
We study $F$purity and strong $F$regularity of blowup algebras. 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 skewsymmetric 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 $F$pure filtrations and symbolic $F$purity.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.00592
 Bibcode:
 2021arXiv210900592D
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Algebraic Geometry;
 13A30;
 13A35;
 13A02;
 13C15
 EPrint:
 This preprint corrects, replaces, and expands the work done in preprint arXiv:2004.03831, which contains a mistake Lemma 5.4