The generalised Mukai conjecture for spherical varieties

Abstract

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.

arXiv commentA question of Gongyo on nef partitions is answered. There are new examples, and the previous version has been split into two separate papers