7 papers
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…
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 Ä…
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 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…
Deformation Theory for Finite Cluster Complexes
Nathan Ilten, Alfredo Nájera Chávez, Hipolito Treffinger
We study the deformation theory of the Stanley-Reisner rings associated to cluster complexes for skew-symmetrizable cluster algebras of geometric and finite cluster type. In partic…
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…