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Dive into the research topics where Alessandro De Stefani is active.

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Featured researches published by Alessandro De Stefani.


arXiv: Commutative Algebra | 2015

Symbolic Powers of Ideals

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

Artinian Level Algebras of Low Socle Degree

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

A Zariski--Nagata theorem for smooth ℤ-algebras

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

Frobenius Betti numbers and modules of finite projective dimension

Alessandro De Stefani; Craig Huneke; Luis Núñez-Betancourt

Let


Nagoya Mathematical Journal | 2018

F-thresholds of graded rings

Alessandro De Stefani; Luis Núñez-Betancourt

(R,\mathfrak{m},K)


Journal of Pure and Applied Algebra | 2016

PRODUCTS OF IDEALS MAY NOT BE GOLOD

Alessandro De Stefani

be a local ring, and let


arXiv: Commutative Algebra | 2016

Globalizing F-invariants

Alessandro De Stefani; Thomas Polstra; Yongwei Yao

M


Transactions of the American Mathematical Society | 2017

On the existence of -thresholds and related limits

Alessandro De Stefani; Luis Núñez-Betancourt; Felipe Pérez

be an


arXiv: Commutative Algebra | 2017

Generalizing Serre’s Splitting Theorem and Bass’s Cancellation Theorem via free-basic elements

Alessandro De Stefani; Thomas Polstra; Yongwei Yao

R


arXiv: Commutative Algebra | 2018

Cohomologically full rings.

Hailong Dao; Alessandro De Stefani; Linquan Ma

-module of finite length. We study asymptotic invariants,

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Luis Núñez-Betancourt

Centro de Investigación en Matemáticas

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Yongwei Yao

Georgia State University

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Eric Canton

University of Nebraska–Lincoln

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