5 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…