9 citations · 56 across the 26 of their papers we have counts for
36 papers
Bounds for Regularity of Toric Varieties in Terms of Multiplicity
Giulio Caviglia, Kieran Hilmer
The Eisenbud-Goto conjecture stated that for a homogeneous prime ideal in a polynomial ring over an algebraically closed field, the Castelnuovo-Mumford regularity is bounded above…
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…
Explicit Stillman bounds for all degrees
Giulio Caviglia, Yihui Liang, Cheng Meng
In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a uniform upper bound on the length of an -sequence containing fixed forms of degree…
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…
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…
Bounds for syzygies of monomial curves
Giulio Caviglia, Alessio Moscariello, Alessio Sammartano
Let G be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of G which depends only on the width of G, that is, the differenc…