9 citations · 43 across the 17 of their papers we have counts for
26 papers
Golod ideals in combinatorial commutative algebra
Benjamin Briggs, Trung Chau, Alessandro De Stefani
In this article we study the Golod property of standard graded algebras. We show that determinantal ideals, binomial edge ideals, and permanental ideals are Golod if and only if th…
Quadratic linear strands of prime ideals
Giulio Caviglia, Alessandro De Stefani
We prove sharp estimates on the quadratic strand of the resolution of any homogeneous prime ideal in a standard graded polynomial ring over an arbitrary field. Our bounds only depe…
Herzog ideals and -singularities
Alessandro De Stefani, Linquan Ma, Matteo Varbaro
In this paper we study the connection between Herzog ideals (i.e., ideals with a squarefree Gröbner degeneration) and -singularities. More precisely, we show that, in positive c…
Uniform bounds on projective dimension and Castelnuovo-Mumford regularity
Giulio Caviglia, Alessandro De Stefani
In this article we obtain uniform effective upper bounds for the projective dimension and the Castelnuovo-Mumford regularity of homogeneous ideals inside a standard graded polynomi…
From a local ring to its associated graded algebra
Alessandro De Stefani, Maria Evelina Rossi, Matteo Varbaro
Let be a complete local ring, and be its associated graded ring. We introduce a homogenization technique which allows to relate $G…
A criterion for sequential Cohen-Macaulayness
Giulio Caviglia, Alessandro De Stefani
The purpose of this note is to show that a finitely generated graded module over , a field, is sequentially Cohen-Macaulay if and only if its arithmeti…
Ladder determinantal varieties and their symbolic blowups
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt +2
In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal is strongly -regular. Furthermore, we prove that the symbolic associated graded alge…
On the notion of sequentially Cohen-Macaulay modules
Giulio Caviglia, Alessandro De Stefani, Enrico Sbarra +1
In this survey paper we first present the main properties of sequentially Cohen-Macaulay modules. Some basic examples are provided to help the reader with quickly getting acquainte…
On the rate of generic Gorenstein -algebras
Mats Boij, Emanuela De Negri, Alessandro De Stefani +1
The rate of a standard graded -algebra is a measure of the growth of the shifts in a minimal free resolution of as an -module. In particular has rate one if and o…
Purity of monoids and characteristic-free splittings in semigroup rings
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt
Inspired by methods in prime characteristic in commutative algebra, we introduce and study combinatorial invariants of seminormal monoids. We relate such numbers with the singulari…
Blowup algebras of determinantal ideals in prime characteristic
Alessandro De Stefani, Jonathan Montaño, Luis Núñez-Betancourt
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…
The Eisenbud-Green-Harris Conjecture
Giulio Caviglia, Alessandro De Stefani, Enrico Sbarra
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of man…
A uniform Chevalley theorem for direct summands of polynomial rings in mixed characteristic
Alessandro De Stefani, Eloísa Grifo, Jack Jeffries
We prove an explicit uniform Chevalley theorem for direct summands of graded polynomial rings in mixed characteristic. Our strategy relies on the introduction of a new type of diff…
F-stable secondary representations and deformation of F-injectivity
Alessandro De Stefani, Linquan Ma
We prove that deformation of F-injectivity holds for local rings that admit secondary representations of which are stable under the natur…
A Cayley-Bacharach theorem for points in
Giulio Caviglia, Alessandro De Stefani
We prove a Cayley-Bacharach-type theorem for points in projective space that lie on a complete intersection of hypersurfaces. This is made possible by new bounds…
Local cohomology and Lyubeznik numbers of -pure rings
Alessandro De Stefani, Eloísa Grifo, Luis Núñez-Betancourt
In this article, we study certain local cohomology modules over -pure rings. We give sufficient conditions for the vanishing of some Lyubeznik numbers, derive a formula for comp…
A Zariski-Nagata theorem for smooth -algebras
Alessandro De Stefani, Eloísa Grifo, Jack Jeffries
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…
Generalizing Serre's Splitting Theorem and Bass's Cancellation Theorem via free-basic elements
Alessandro De Stefani, Thomas Polstra, Yongwei Yao
We give new proofs of two results of Stafford, which generalize two famous Theorems of Serre and Bass regarding projective modules. Our techniques are inspired by the theory of bas…
Globalizing F-invariants
Alessandro De Stefani, Thomas Polstra, Yongwei Yao
In this paper we define and study the global Hilbert-Kunz multiplicity and the global F-signature of prime characteristic rings which are not necessarily local. Our techniques are…
On the behavior of singularities at the -pure threshold
Eric Canton, Daniel Hernández, Karl Schwede +6
We provide a family of examples where the -pure threshold and the log canonical threshold of a polynomial are different, but where does not divide the denominator of the …
F-thresholds of graded rings
Alessandro De Stefani, Luis Núñez-Betancourt
The a-invariant, the F-pure threshold, and the diagonal F-threshold are three important invariants of a graded K-algebra. Hirose, Watanabe, and Yoshida have conjectured relations a…
A counterexample to a conjecture of Ding
Alessandro De Stefani
We give a counterexample to a conjecture posed by S. Ding regarding the index of a Gorenstein local ring by exhibiting several examples of one dimensional local complete intersecti…
Products of ideals may not be Golod
Alessandro De Stefani
We exhibit an example of a product of two proper monomial ideals such that the residue class ring is not Golod. We also discuss the strongly Golod property for rational powers of m…
An algorithm for constructing certain differential operators in positive characteristic
Alberto F. Boix, Alessandro De Stefani, Davide Vanzo
Given a non-zero polynomial in a polynomial ring with coefficients in a finite field of prime characteristic , we present an algorithm to compute a differential operator…