Alessandro De Stefani
University of Nebraska–Lincoln
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Featured researches published by Alessandro De Stefani.
arXiv: Commutative Algebra | 2015
Hailong Dao; Alessandro De Stefani; Eloísa Grifo; Craig Huneke; Luis Núñez-Betancourt
We survey classical and recent results on symbolic powers of ideals. We focus on properties and problems of symbolic powers over regular rings, on the comparison of symbolic and regular powers, and on the combinatorics of the symbolic powers of monomial ideals. In addition, we present some new results on these aspects of the subject.
Communications in Algebra | 2014
Alessandro De Stefani
In this article we study Hilbert functions and isomorphism classes of Artinian level local algebras via Macaulays inverse system. Upper and lower bounds concerning numerical functions admissible for level algebras of fixed type and socle degree are known. For each value in this range we exhibit a level local algebra with that Hilbert function, provided that the socle degree is at most three. Furthermore, we prove that level local algebras of socle degree three and maximal Hilbert function are graded. In the graded case, the extremal strata have been parametrized by Cho and Iarrobino.
Crelle's Journal | 2018
Alessandro De Stefani; Eloísa Grifo; Jack Jeffries
Abstract In a polynomial ring over a perfect field, the symbolic powers of a prime ideal can be described via differential operators: a classical result by Zariski and Nagata says that the n-th symbolic power of a given prime ideal consists of the elements that vanish up to order n on the corresponding variety. However, this description fails in mixed characteristic. In this paper, we use p-derivations, a notion due to Buium and Joyal, to define a new kind of differential powers in mixed characteristic, and prove that this new object does coincide with the symbolic powers of prime ideals. This seems to be the first application of p-derivations to commutative algebra.
Journal of Commutative Algebra | 2017
Alessandro De Stefani; Craig Huneke; Luis Núñez-Betancourt
Let
Nagoya Mathematical Journal | 2018
Alessandro De Stefani; Luis Núñez-Betancourt
(R,\mathfrak{m},K)
Journal of Pure and Applied Algebra | 2016
Alessandro De Stefani
be a local ring, and let
arXiv: Commutative Algebra | 2016
Alessandro De Stefani; Thomas Polstra; Yongwei Yao
M
Transactions of the American Mathematical Society | 2017
Alessandro De Stefani; Luis Núñez-Betancourt; Felipe Pérez
be an
arXiv: Commutative Algebra | 2017
Alessandro De Stefani; Thomas Polstra; Yongwei Yao
R
arXiv: Commutative Algebra | 2018
Hailong Dao; Alessandro De Stefani; Linquan Ma
-module of finite length. We study asymptotic invariants,