19 citations · 54 across the 8 of their papers we have counts for
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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…
Luna-Vust invariants of Cox rings and skeletons of spherical varieties
Giuliano Gagliardi
Given the Luna-Vust invariants of a spherical variety, we determine the Luna-Vust invariants of the spectrum of its Cox ring. In particular, we deduce an explicit description of th…
The generalized Mukai conjecture for symmetric varieties
Giuliano Gagliardi, Johannes Hofscheier
We associate to any complete spherical variety a certain nonnegative rational number , which we conjecture to satisfy the inequality $\wp(X) \le \operatorname{dim} X -…
Homogeneous spherical data of orbits in spherical embeddings
Giuliano Gagliardi, Johannes Hofscheier
Let be a connected reductive complex algebraic group. Luna assigned to any spherical homogeneous space a combinatorial object called a homogeneous spherical datum. By a t…
A combinatorial smoothness criterion for spherical varieties
Giuliano Gagliardi
We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Ca…
Gorenstein spherical Fano varieties
Giuliano Gagliardi, Johannes Hofscheier
We obtain a combinatorial description of Gorenstein spherical Fano varieties in terms of certain polytopes, generalizing the combinatorial description of Gorenstein toric Fano vari…
The Cox ring of a spherical embedding
Giuliano Gagliardi
Let G be a connected reductive group and G/H a spherical homogeneous space. We show that the ideal of relations between a natural set of generators of the Cox ring of a G-embedding…