Alessio Sammartano

activity

20102026

most citedNumerical semigroups with large embedding dimension satisfy Wilf's conjecture

30 citations · 148 across the 30 of their papers we have counts for

collaborators

Showing math.ACShow all

21 papers · 1 filter

math.AC2026

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…

math.AC2026

Behrend function and blowup algebras

Claudia Polini, Alessio Sammartano, Bernd Ulrich

Given a scheme $X$ of finite type over the complex numbers, the Behrend function is a constructible function $ν_{X} : X (C) \to Z$ introduced by Behrend in ord…

math.AC2025

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…

math.AC2025

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…

math.AC2023★ 1 cited

Higher resonance schemes and Koszul modules of simplicial complexes

Marian Aprodu, Gavril Farkas, Claudiu Raicu +2

Each connected graded, graded-commutative algebra $A$ of finite type over a field $k$ of characteristic zero defines a complex of finitely generated, graded modules over a symm…

math.AC2023★ 3 cited

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…

math.AC2022★ 1 cited

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…

math.AC2021★ 4 cited

Rational singularities of nested Hilbert schemes

Ritvik Ramkumar, Alessio Sammartano

The Hilbert scheme of points $Hilb^{n} (S)$ of a smooth surface $S$ is a well-studied parameter space, lying at the interface of algebraic geometry, commutative algebra, repr…

math.AC2019★ 6 cited

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…

math.AC2019★ 4 cited

Syzygies in Hilbert schemes of complete intersections

Giulio Caviglia, Alessio Sammartano

Let $e_{1}, ..., e_{c}$ be positive integers and let $Y \subseteq P^{n}$ be the monomial complete intersection defined by the vanishing of $x_{1}^{e_{1}}, ..., x_{c}^{e_{c}}$ . In thi…

math.AC2018★ 5 cited

On the Lex-plus-powers Conjecture

Giulio Caviglia, Alessio Sammartano

Let $S$ be a polynomial ring over a field and $I \subseteq S$ a homogeneous ideal containing a regular sequence of forms of degrees $d_{1}, \dots, d_{c}$ . In this paper we prove the Le…

math.AC2017

On the multiplicity of tangent cones of monomial curves

Alessio Sammartano

Let $Λ$ be a numerical semigroup, $C \subseteq A^{n}$ the monomial curve singularity associated to $Λ$ , and $T$ its tangent cone. In this paper we provide…

math.AC2016★ 8 cited

Blowup algebras of rational normal scrolls

Alessio Sammartano

We determine the equations of the blowup of $P^{n}$ along a $d$ -fold rational normal scroll $S$ , and we prove that the Rees ring and special fiber ring of $S \subseteq \math…

math.AC2016★ 2 cited

Consecutive cancellations in Tor modules over local rings

Alessio Sammartano

Let $M, N$ be finite modules over a Noetherian local ring $R$ , and let $G$ be the associated graded ring of $R$ . We show that the bigraded Hilbert series of $g r (T o r^{R} (M, N))$ is obt…

math.AC2015

Edge ideals and DG algebra resolutions

Adam Boocher, Alessio D'Alì, Eloísa Grifo +2

Let $R = S / I$ where $S = k [T_{1}, \dots, T_{n}]$ and $I$ is a homogeneous ideal in $S$ . The acyclic closure $R ⟨ Y ⟩$ of $k$ over $R$ is a DG algebra resolution obtained by…

math.AC2015★ 2 cited

On the growth of deviations

Adam Boocher, Alessio D'Alì, Eloísa Grifo +2

The deviations of a graded algebra are a sequence of integers that determine the Poincare series of its residue field and arise as the number of generators of certain DG algebras.…

math.AC2013★ 13 cited

Classes of complete intersection numerical semigroups

Marco D'Anna, Vincenzo Micale, Alessio Sammartano

We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and fa…

math.AC2012

s-Hankel hypermatrices and 2 x 2 determinantal ideals

Alessio Sammartano

We introduce the concept of s-Hankel hypermatrix, which generalizes both Hankel matrices and generic hypermatrices. We study two determinantal ideals associated to an s-Hankel hype…

math.AC2011★ 30 cited

Numerical semigroups with large embedding dimension satisfy Wilf's conjecture

Alessio Sammartano

We give an affirmative answer to Wilf's conjecture for numerical semigroups satisfying 2 ν\geq m, where νand m are respectively the embedding dimension and the multiplicity of a se…

math.AC2011★ 28 cited

When the associated graded ring of a semigroup ring is Complete Intersection

Marco D'Anna, Vincenzo Micale, Alessio Sammartano

Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In parti…

math.AC2010★ 10 cited

On the associated graded ring of a semigroup ring

Marco D'Anna, Vincenzo Micale, Alessio Sammartano

Let (R;m) be a numerical semigroup ring. In this paper we study the properties of its associated graded ring G(m). In particular, we describe the H^0_M for G(m) (where M is the hom…