5 papers
Toricness and smoothness criteria for spherical varieties
Giuliano Gagliardi, Johannes Hofscheier, Heath Pearson
We prove equivalent numerical conditions for a complete spherical variety to admit a toric structure, and for the smoothness of an arbitrary spherical variety along any given G-orb…
The generalised Mukai conjecture for spherical varieties
Giuliano Gagliardi, Johannes Hofscheier, Heath Pearson
We prove the generalised Mukai conjecture for -factorial spherical Fano varieties. In this case, a stronger inequality holds featuring an extra term - the minimum absol…
Is there a smooth lattice polytope which does not have the integer decomposition property?
Johannes Hofscheier, Alexander Kasprzyk
We introduce Tadao Oda's famous question on lattice polytopes which was originally posed at Oberwolfach in 1997 and, although simple to state, has remained unanswered. The question…
Examples of IDP lattice polytopes with non-log-concave -vector
Johannes Hofscheier, Vadym Kurylenko, Benjamin Nill
Lattice polytopes are called IDP polytopes if they have the integer decomposition property, i.e., any lattice point in a th dilation is a sum of lattice points in the polyto…
Classification and Ehrhart Theory of Denominator 2 Polygons
Girtrude Hamm, Johannes Hofscheier, Alexander Kasprzyk
We present an algorithm for growing the denominator polygons containing a fixed number of lattice points and enumerate such polygons containing few lattice points for small …