Badescu, Lucian, Valla, Giuseppe
Using the Grothendieck-Lefschetz theory (see \cite{[SGA2]}) we prove a criterion to deduce that certain subvarieties of $\mathbb P^n$ of dimension $\geq 2$ are not set-theoretic complete...
Isomorphism classes of certain complete intersections (2008)
In this paper we classify, up to analytic isomorphism, the family of almost stretched Artinian complete intersection A=R/I with a given Hilbert function, in the case R is a power series ring in two...
A family of local rings with rational Poincar\'e Series (2008)
In this note we compute the Poincare Series of almost stretched Gorenstein local rings. It turns out that it is rational
Structure theorems for certain Gorenstein ideals (2007)
The main achievement of this paper is to provide a structure theorem for Artinian, Gorenstein local rings with the property that the square of the maximal ideal is generated by two elements. The...
Canonical Hilbert-Burch matrices for ideals of $k[x,y]$ (2007)
An Artinian ideal $I$ of $k[x,y]$ has many Hilbert-Burch matrices. We show that there is a canonical choice. As an application, we determine the dimension of certain affine Gr\"obner cells and their...
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...
The dimension of certain catalectiant varieties (2004)
Let $V_{s,t}$ be the rank $\leq s$ locus in $\mathbb{P}^{{2t+2\choose 2 }-1}$ of the generic catalecticant matrix Cat$(t, t; 3)$. This matrix has rather more symmetry than a generic symmetric matrix;...
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...
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...
Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces (1997)
Conca, Aldo., Valla, Giuseppe., Herzog, Jurgen., Trung, Ngo Viet.
American Journal of Mathematics - Volume 119, Number 4, August 1997