7 citations · 7 across the 1 of their papers we have counts for
6 papers
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…
Algebraic Hyperbolicity for Surfaces in Toric Threefolds
Christian Haase, Nathan Ilten
Adapting focal loci techniques used by Chiantini and Lopez, we provide lower bounds on the genera of curves contained in very general surfaces in Gorenstein toric threefolds. We il…
Deformations of Smooth Complete Toric Varieties: Obstructions and the Cup Product
Nathan Ilten, Charles Turo
Let be a complete -factorial toric variety. We explicitly describe the space and the cup product map in com…
Projective duals to algebraic and tropical hypersurfaces
Nathan Ilten, Yoav Len
We study a tropical analogue of the projective dual variety of a hypersurface. When is a curve in or a surface in , we provide an explicit descript…
Fujita's Freeness Conjecture for -Varieties of Complexity One
Klaus Altmann, Nathan Ilten
We prove Fujita's freeness conjecture for Gorenstein complexity-one -varieties with rational singularities.
One-Parameter Toric Deformations of Cyclic Quotient Singularities
Nathan Ilten
In the case of two-dimensional cyclic quotient singularities, we classify all one-parameter toric deformations in terms of certain Minkowski decompositions. In particular, we descr…