11 citations · 57 across the 23 of their papers we have counts for
13 papers · 1 filter
Homogeneous Border Bases on Infinite Order Ideals
Cristina Bertone, Sofia Bovero
Border bases are traditionally restricted to 0-dimensional ideals due to the finiteness of the underlying order ideal. In this paper we extend the theory to homogeneous ideals of p…
Free resolutions and marked families
Cristina Bertone, Francesca Cioffi, Paolo Lella
Let be a field and a Noetherian -algebra. In a paper of 2020, M. Albert, C. Bertone, M. Roggero and W. M. Seiler proved that, given a quasi-stable modu…
Cohen-Macaulay, Gorenstein and complete intersection conditions by marked bases
Cristina Bertone, Francesca Cioffi, Matthias Orth +1
Using techniques coming from the theory of marked bases, we develop new computational methods for detection and construction of Cohen-Macaulay, Gorenstein and complete intersection…
Open Covers and Lex Points of Hilbert schemes over quotient rings via relative marked bases
Cristina Bertone, Francesca Cioffi, Matthias Orth +1
We introduce the notion of a relative marked basis over quasi-stable ideals, together with constructive methods and a functorial interpretation, developing computational methods fo…
The close relation between border and Pommaret marked bases
Cristina Bertone, Francesca Cioffi
Given a finite order ideal in the polynomial ring over a field , let be the border of and $\mathcal P_{\mathc…
On almost revlex ideals with Hilbert function of complete intersections
Cristina Bertone, Francesca Cioffi
In this paper, we investigate the behavior of almost reverse lexicographic ideals with the Hilbert function of a complete intersection. More precisely, over a field , we give a…