5 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…
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…
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…