arXiv subjects

Heath Pearson

Publications and source records attributed to Heath Pearson.

3 recordsLinked to original sources

arXiv2026

The Mukai conjecture via Cox rings for special toric ambient embeddings

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 their Cox rings. The Fano varieties of this class are characterised in terms of the property that they admit an embedding into a smooth projective toric variety via the bunched ring theory of Mori dream spaces. Our approach inherits the Mukai conjecture for this class from a log version of the Mukai conjecture on the toric ambient embedding.

math.AG↗

arXiv2026

Toricness and smoothness criteria for spherical varieties

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-orbit. The conditions are in terms of spherical skeletons, a coarse ''subset'' of the Luna-Vust data of a spherical variety. Our smoothness criterion improves upon classical criteria by removing the dependency on external reference tables.

math.AG↗

arXiv2025

The generalised Mukai conjecture for spherical varieties

We prove the generalised Mukai conjecture for $\mathbb{Q}$-factorial spherical Fano varieties. In this case, a stronger inequality holds featuring an extra term - the minimum absolute complexity of a log Calabi-Yau pair - which measures how close the Fano variety is to being toric.

math.AG↗