30 citations · 148 across the 30 of their papers we have counts for
31 papers
The structure of almost symmetric almost complete intersection numerical semigroups
Kazufumi Eto, Naoyuki Matsuoka, Alessio Moscariello +3
We prove a structure theorem for numerical semigroups H that are almost symmetric and almost complete intersections. We show that a row-factorization (RF) matrix of H must possess…
Behrend function and blowup algebras
Claudia Polini, Alessio Sammartano, Bernd Ulrich
Given a scheme of finite type over the complex numbers, the Behrend function is a constructible function introduced by Behrend in ord…
The variety of orthogonal frames
Laura Casabella, Alessio Sammartano
An orthogonal n-frame is an ordered set of n pairwise orthogonal vectors. The set of all orthogonal n-frames in a d-dimensional quadratic vector space is an algebraic variety V(d,n…
Initial ideals of weighted forms and the genus of locally Cohen-Macaulay curves
Alessio Sammartano, Enrico Schlesinger
Let C be a locally Cohen-Macaulay curve in complex projective 3-space. The maximum genus problem predicts the largest possible arithmetic genus g(d,s) that C can achieve assuming t…
The Hilbert scheme of points on a threefold: broken Gorenstein structures and linkage
Joachim Jelisiejew, Ritvik Ramkumar, Alessio Sammartano
We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees s…
Open problems on relations of numerical semigroups
Alessio Moscariello, Alessio Sammartano
We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and assoc…
On minimal presentations of numerical monoids
Alessio Moscariello, Alessio Sammartano
We consider the classical problem of determining the largest possible cardinality of a minimal presentation of a numerical monoid with given embedding dimension and multiplicity. V…
Irrational components of the Hilbert scheme of points
Gavril Farkas, Rahul Pandharipande, Alessio Sammartano
We construct irrational irreducible components of the Hilbert scheme of points of affine n-dimensional space, for n at least 12. We start with irrational components of the Hilbert…
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…
Higher resonance schemes and Koszul modules of simplicial complexes
Marian Aprodu, Gavril Farkas, Claudiu Raicu +2
Each connected graded, graded-commutative algebra of finite type over a field of characteristic zero defines a complex of finitely generated, graded modules over a symm…
Bounds for syzygies of monomial curves
Giulio Caviglia, Alessio Moscariello, Alessio Sammartano
Let G be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of G which depends only on the width of G, that is, the differenc…
On the parity conjecture for Hilbert schemes of points on threefolds
Ritvik Ramkumar, Alessio Sammartano
Let be the Hilbert scheme of points in , and let denote the tangent space to a point . Okounkov and Pandharipande have conjectured t…
On Rees algebras of 2-determinantal ideals
Ritvik Ramkumar, Alessio Sammartano
Let I be the ideal of minors of a 2 by n matrix of linear forms with the expected codimension. In this paper we prove that the Rees algebra of I and its special fiber ring are Cohe…
Rational singularities of nested Hilbert schemes
Ritvik Ramkumar, Alessio Sammartano
The Hilbert scheme of points of a smooth surface is a well-studied parameter space, lying at the interface of algebraic geometry, commutative algebra, repr…
On the smoothness of lexicographic points on Hilbert schemes
Ritvik Ramkumar, Alessio Sammartano
We study the geometry of standard graded Hilbert schemes of polynomial rings and exterior algebras. Our investigation is motivated by a famous theorem of Reeves and Stillman for th…
On the tangent space to the Hilbert scheme of points in P3
Ritvik Ramkumar, Alessio Sammartano
In this paper we study the tangent space to the Hilbert scheme , motivated by Haiman's work on and by a long-standing c…
Relations between the 2x2 minors of a generic matrix
Hang Huang, Michael Perlman, Claudia Polini +2
We prove the case t = 2 of a conjecture of Bruns-Conca-Varbaro, describing the minimal relations between the t x t minors of a generic matrix. Interpreting these relations as polyn…
Syzygies in Hilbert schemes of complete intersections
Giulio Caviglia, Alessio Sammartano
Let be positive integers and let be the monomial complete intersection defined by the vanishing of . In thi…
Correspondence scrolls
David Eisenbud, Alessio Sammartano
This paper initiates the study of a class of schemes that we call correspondence scrolls, which includes the rational normal scrolls and linearly embedded projective bundle of deco…
On the Lex-plus-powers Conjecture
Giulio Caviglia, Alessio Sammartano
Let be a polynomial ring over a field and a homogeneous ideal containing a regular sequence of forms of degrees . In this paper we prove the Le…
On the multiplicity of tangent cones of monomial curves
Alessio Sammartano
Let be a numerical semigroup, the monomial curve singularity associated to , and its tangent cone. In this paper we provide…
Blowup algebras of rational normal scrolls
Alessio Sammartano
We determine the equations of the blowup of along a -fold rational normal scroll , and we prove that the Rees ring and special fiber ring of $S \subseteq \math…
Consecutive cancellations in Tor modules over local rings
Alessio Sammartano
Let be finite modules over a Noetherian local ring , and let be the associated graded ring of . We show that the bigraded Hilbert series of is obt…
Edge ideals and DG algebra resolutions
Adam Boocher, Alessio D'Alì, Eloísa Grifo +2
Let where and is a homogeneous ideal in . The acyclic closure of over is a DG algebra resolution obtained by…