30 citations · 148 across the 30 of their papers we have counts for
7 papers · 1 filter
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…
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…
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 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…
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…