3 papers
math.AG2026
The Mukai conjecture via Cox rings for special toric ambient embeddings
Heath Pearson
We prove the Mukai conjecture on the characterisation of products of projective spaces among Fano varieties for a class of locally factorial Fano varieties defined in terms of thei…
math.AG2026
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…
math.AG2025
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…