5 papers · 1 filter
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…
Spherical amoebae and a spherical logarithm map
Victor Batyrev, Megumi Harada, Johannes Hofscheier +1
Let be a connected reductive algebraic group over with a maximal compact subgroup . Let be a (quasi-affine) spherical homogeneous space. In the first part…
Cohomology rings of toric bundles and the ring of conditions
Johannes Hofscheier, Askold Khovanskii, Leonid Monin
The celebrated BKK Theorem expresses the number of roots of a system of generic Laurent polynomials in terms of the mixed volume of the corresponding system of Newton polytopes.Puk…
Containment Relations among Spherical Subgroups
Johannes Hofscheier
A closed subgroup of a connected reductive group is called if a Borel subgroup in has an open orbit on . We give a combinatorial characterizat…