Isomorphism classes of short Gorenstein local rings via Macaulay's inverse system (2009)
Elias, Joan, Rossi, Maria Evelina
In this paper we study the isomorphism classes of Artinian Gorenstein local rings with socle degree three by means of Macaulay's inverse system. We prove that their classification is equivalent to...
Consecutive cancellations in Betti numbers of local rings (2009)
Rossi, Maria Evelina, Sharifan, Leila
Let I be a homogeneous ideal in a polynomial ring P over a field. By Macaulay's Theorem, there exists a lexicographic ideal L=Lex(I) with the same Hilbert function as I. Peeva has proved that the...
Theory Theory Theory Theory Theory Theory Theory Theory Theory (2008)
Aldo Conca, Emanuela De Negri, Maria Evelina Rossi
Number Number Number Number Number Number Number Number Number Number
Integrally closed and componentwise linear ideals (2008)
Conca, Aldo, De Negri, Emanuela, Rossi, Maria Evelina
In two dimensional regular local rings integrally closed ideals have a unique factorization property and have a Cohen-Macaulay associated graded ring. In higher dimension these properties do not hold...
An algorithm for the Hilbert-Samuel function of a primary ideal (2007)
Let R be a noetherian local ring of dimension d, m its maximal ideal, K = R=m the residue field. If I is an m-primary ideal, then l R (R=I) is finite, each I
Contracted ideals and the Groebner fan of the rational normal curve (2007)
Conca, Aldo, De Negri, Emanuela, Rossi, Maria Evelina
The paper has two goals: the study the associated graded ring of contracted homogeneous ideals in $K[x,y]$ and the study of the Groebner fan of the ideal $P$ of the rational normal curve in ${\bf...
Castelnuovo-Mumford Regularity and finiteness of Hilbert Functions (2004)
Rossi, Maria Evelina, Trung, Ngo Viet, Valla, Giuseppe
The notion of regularity has been used by S. Kleiman in the construction of bounded families of ideals or sheaves with given Hilbert polynomial, a crucial point in the construction of Hilbert or...
Graded rings associated with contracted ideals (2004)
Conca, Aldo, De Negri, Emanuela, Jayanthan, A. V., Rossi, Maria Evelina
By definition, an $\m$-primary ideal $I$ in a 2-dimensional regular local ring $(R, \m)$ is contracted if $I=R \cap IR[\m/x]$ for some $x \in \m \setminus \m^2$. Contracted ideals have been...
Depth of associated graded rings via Hilbert coefficients of ideals (2003)
Corso, Alberto, Polini, Claudia, Rossi, Maria Evelina
Given a local Cohen-Macaulay ring $(R, {\mathfrak m})$, we study the interplay between the integral closedness -- or even the normality -- of an ${\mathfrak m}$-primary $R$-ideal $I$ and conditions...
Castelnuovo-Mumford regularity and extended degree (2002)
Rossi, Maria Evelina, Trung, Ngo Viet, Valla, Giuseppe
The main result of this paper shows that the Castelnuovo-Mumford regularity of the tangent cone of a local ring is effectively bounded by the dimension and any extended degree. From this it follows...
Notes on the behavior of the Ratliff-Rush filtration (2002)
Rossi, Maria Evelina, Swanson, Irena
We establish new classes of Ratliff-Rush closed ideals and some pathological behavior of the Ratliff-Rush closure. In particular, Ratliff-Rush closure does not behave well under passage modulo...
COHEN±MACAULAY LOCAL RINGS OF EMBEDDING DIMENSION e‡d 3 (1998)
Maria Evelina Rossi, Giuseppe Valla
The Hilbert function HA…n † of a local ring …A; m † is a good measure of the singularity at…A; m†: We can say that this numerical function describes the degree to which A deviates from a...