10 papers
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…