8 citations · 23 across the 19 of their papers we have counts for
26 papers
Components of the nested Hilbert scheme of few points
Michele Graffeo, Paolo Lella
We study the existence and the schematic structure of elementary components of the nested Hilbert scheme on a smooth quasi-projective variety. Precisely, we find a new lower bound…
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…
New components of Hilbert schemes of points and 2-step ideals
Franco Giovenzana, Luca Giovenzana, Michele Graffeo +1
This paper presents new examples of elementary and non-elementary irreducible components of the Hilbert scheme of points and its nested variants. The results are achieved via a car…
Unexpected but recurrent phenomena for Quot and Hilbert schemes of points
Franco Giovenzana, Luca Giovenzana, Michele Graffeo +1
We investigate some aspects of the geometry of two classical generalisations of the Hilbert schemes of points. Precisely, we show that parity conjecture for $\text{Quot}_r^d\mathbb…
The geometry of double nested Hilbert schemes of points on curves
Michele Graffeo, Paolo Lella, Sergej Monavari +2
Let be a smooth curve. In this paper we investigate the geometric properties of the double nested Hilbert scheme of points on , a moduli space introduced by the third author…
A counterexample to the parity conjecture
Franco Giovenzana, Luca Giovenzana, Michele Graffeo +1
Let be a zero-dimensional subscheme of the affine three-dimensional complex space of length . Okounkov and Pandharipande have conjectured tha…
The Gröbner fan of the Hilbert scheme
Yuta Kambe, Paolo Lella
We give a notion of "combinatorial proximity" among strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. We show that this notion guarantees "geometri…
The maximum genus problem for locally Cohen-Macaulay space curves
Valentina Beorchia, Paolo Lella, Enrico Schlesinger
Let denote the maximum arithmetic genus of a locally Cohen-Macaulay curve of degree in that is not contained in a surface of degree . A…
A construction of equivariant bundles on the space of symmetric forms
Ada Boralevi, Daniele Faenzi, Paolo Lella
We construct stable vector bundles on the space of symmetric forms of degree d in n+1 variables which are equivariant for the action of SL_{n+1}(C), and admit an equivariant free r…
Towards Fulton's conjecture
Claudio Fontanari, Riccardo Ghiloni, Paolo Lella
We present an alternate proof, much quicker and more straightforward than the original one, of a celebrated Fulton's conjecture on the ample cone of the moduli space of stable rati…
Truncated modules and linear presentations of vector bundles
Ada Boralevi, Daniele Faenzi, Paolo Lella
We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of…
Strongly stable ideals and Hilbert polynomials
Davide Alberelli, Paolo Lella
The \texttt{StronglyStableIdeals} package for \textit{Macaulay2} provides a method to compute all saturated strongly stable ideals in a given polynomial ring with a fixed Hilbert p…
The maximum likelihood degree of Fermat hypersurfaces
Daniele Agostini, Davide Alberelli, Francesco Grande +1
We study the critical points of the likelihood function over the Fermat hypersurface. This problem is related to one of the main problems in statistical optimization: maximum likel…
A combinatorial description of finite O-sequences and aCM genera
Francesca Cioffi, Paolo Lella, Maria Grazia Marinari
The goal of this paper is to explicitly detect all the arithmetic genera of arithmetically Cohen-Macaulay projective curves with a given degree . It is well-known that the arith…
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…
Smooth curves specialize to extremal curves
Robin Hartshorne, Paolo Lella, Enrico Schlesinger
Let denote the Hilbert scheme of locally Cohen-Macaulay curves of degree and genus in projective three space. We show that, given a smooth irreducible curve o…
An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme
Paolo Lella
Borel-fixed ideals play a key role in the study of Hilbert schemes. Indeed each component and each intersection of components of a Hilbert scheme contains at least one Borel-fixed…
Computable Hilbert Schemes
Paolo Lella
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In C…
The Hilbert schemes of locally Cohen-Macaulay curves in P^3 may after all be connected
Paolo Lella, Enrico Schlesinger
Progress on the problem whether the Hilbert schemes of locally Cohen-Macaulay curves in projective 3 space are connected has been hampered by the lack of an answer to a question th…
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…
A network of rational curves on the Hilbert scheme
Paolo Lella
In this paper we introduce an effective method to construct rational deformations between couples of Borel-fixed ideals. These deformations are governed by flat families, so that t…
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…