33 citations · 132 across the 22 of their papers we have counts for
27 papers
On the Quot scheme
Cristina Bertone, Steven L. Kleiman, Margherita Roggero
We consider the quot scheme of locally free quotients of with Hilbert po…
Smoothable Gorenstein points via marked schemes and double-generic initial ideals
Cristina Bertone, Francesca Cioffi, Margherita Roggero
Over an infinite field with , we investigate smoothable Gorenstein -points in a punctual Hilbert scheme and obtain the following results: (i) every…
Quivers and equations a la Plücker for the Hilbert scheme
Laurent Evain, Margherita Roggero
Several moduli spaces parametrizing linear subspaces of the projective space are cut out by linear and quadratic equations in their natural embedding: Grassmannians, Flag varieties…
Minimum-weight codewords of the Hermitian codes are supported on complete intersections
Chiara Marcolla, Margherita Roggero
Let be the Hermitian curve defined over a finite field . In this paper we complete the geometrical characterization of the supports of the minimum-w…
Computing Quot schemes via marked bases over quasi-stable modules
Mario Albert, Cristina Bertone, Margherita Roggero +1
Let be a field of arbitrary characteristic, a Noetherian -algebra and consider the polynomial ring . We consider homogeneous sub…
A general framework for Noetherian well ordered polynomial reductions
Michela Ceria, Teo Mora, Margherita Roggero
Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an e…
Hermitian codes and complete intersections
Chiara Marcolla, Margherita Roggero
In this paper we present a geometrical characterization for the minimum-weight codewords of the Hermitian codes over the fields in the third and fourth phase, na…
Double-Generic Initial Ideal and Hilbert Scheme
Cristina Bertone, Francesca Cioffi, Margherita Roggero
Following the approach in the book "Commutative Algebra", by D. Eisenbud, where the author describes the generic initial ideal by means of a suitable total order on the terms of an…
The scheme of liftings and applications
Cristina Bertone, Francesca Cioffi, Margherita Guida +1
We study the locus of the liftings of a homogeneous ideal in a polynomial ring over any field. We prove that this locus can be endowed with a structure of scheme …
Term-ordering free involutive bases
Michela Ceria, Teo Mora, Margherita Roggero
In this paper, we consider a monomial ideal J in P := A[x1,...,xn], over a commutative ring A, and we face the problem of the characterization for the family Mf(J) of all homogeneo…
On the functoriality of marked families
Paolo Lella, Margherita Roggero
The application of methods of computational algebra has recently introduced new tools for the study of Hilbert schemes. The key idea is to define flat families of ideals endowed wi…
Minimal Castelnuovo-Mumford regularity for a given Hilbert polynomial
Francesca Cioffi, Paolo Lella, M. Grazia Marinari +1
Let be an algebraically closed field of null characteristic and a Hilbert polynomial. We look for the minimal Castelnuovo-Mumford regularity of closed subsche…
Macaulay-like marked bases
Cristina Bertone, Francesca Cioffi, Margherita Roggero
We define marked sets and bases over a quasi-stable ideal in a polynomial ring on a Noetherian -algebra, with a field of any characteristic. The involved polyn…
Borel Degenerations of Arithmetically Cohen-Macaulay curves in P^3
Gunnar Floystad, Margherita Roggero
We investigate Borel ideals on the Hilbert scheme components of arithmetically Cohen-Macaulay (ACM) codimension two schemes in P^n. We give a basic necessary criterion for a Borel…
The locus of points of the Hilbert scheme with bounded regularity
Edoardo Ballico, Cristina Bertone, Margherita Roggero
In this paper we consider the Hilbert scheme parameterizing subschemes of with Hilbert polynomial , and we investigate its locus containing points corre…
Upgraded methods for the effective computation of marked schemes on a strongly stable ideal
Cristina Bertone, Francesca Cioffi, Paolo Lella +1
Let be a monomial strongly stable ideal. The collection $\Mf(J)$ of the homogeneous polynomial ideals , such that the monomials outside form a $K…
Extensors and the Hilbert scheme
Jerome Brachat, Paolo Lella, Bernard Mourrain +1
The Hilbert scheme parametrizes closed subschemes and families of closed subschemes in the projective space with a fixed Hilbert polynomia…
Flat families by strongly stable ideals and a generalization of Groebner bases
Francesca Cioffi, Margherita Roggero
Let J be a strongly stable monomial ideal in S=K[x_1,...,x_n] and let Mf(J) be the family of all homogeneous ideals I in S such that the set of all terms outside J is a K-vector ba…
The stratum of a strongly stable ideal
Margherita Roggero
Let J be a strongly stable monomial ideal in P=k[X0,...,Xn] and let BSt(J) be the family of all the homogeneous ideals in P such that the set N(J) of all the monomials that do not…
Segments and Hilbert schemes of points
Francesca Cioffi, Paolo Lella, Maria Grazia Marinari +1
Using results obtained from the study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a…
A Borel open cover of the Hilbert scheme
Cristina Bertone, Paolo Lella, Margherita Roggero
Let be an admissible Hilbert polynomial in $\PP^n$ of degree . The Hilbert scheme $\hilb^n_p(t)$ can be realized as a closed subscheme of a suitable Grassmannian $ \mathb…
Conchoidal transform of two plane curves
Alberto Albano, Margherita Roggero
The conchoid of a plane curve is constructed using a fixed circle in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of…
Rational components of Hilbert schemes
Paolo Lella, Margherita Roggero
The Gröbner stratum of a monomial ideal $\id{j}$ is an affine variety that parametrizes the family of all ideals having $\id{j}$ as initial ideal (with respect to a fixed term orde…
Homogeneous varieties for Hilbert schemes
Giorgio Ferrarese, Margherita Roggero
The paper concerns the affine varieties that are homogeneous with respect to a (non-standard) graduation over the group Z^m. Among the other properties it is shown that every such…