7 citations · 7 across the 4 of their papers we have counts for
11 papers · 1 filter
Higher cotangent cohomology for Stanley-Reisner rings
Nathan Ilten, Francesco Meazzini, Andrea Petracci
Inspired by work of Altmann and Christophersen, we study the graded pieces of the cotangent cohomology , of the Stanley-Reisner ring $S_{\mathcal{K…
Local Equations for Hilbert Schemes of Points
Nathan Ilten, Francesco Meazzini, Andrea Petracci
We compute the completion of the local ring of the Hilbert scheme of degree subschemes of at the point corresponding to the ideal $\langle x_1,\ldots,x_n\rangl…
Locally Trivial Deformations of Toric Varieties
Nathan Ilten, Sharon Robins
We study locally trivial deformations of toric varieties from a combinatorial point of view. For any fan , we construct a deformation functor by considering Čec…
Rational Curves in Projective Toric Varieties
Nathan Ilten, Jake Levinson
We study embedded rational curves in projective toric varieties. Generalizing results of the first author and Zotine for the case of lines, we show that any degree rational cur…
Local Euler characteristics of -singularities and their application to hyperbolicity
Nils Bruin, Nathan Ilten, Zhe Xu
Wahl's local Euler characteristic measures the local contributions of a singularity to the usual Euler characteristic of a sheaf. Using tools from toric geometry, we study the loca…
Singular Curves of Low Degree and Multifiltrations from Osculating Spaces
Jarosław Buczyński, Nathan Ilten, Emanuele Ventura
In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occu…