The generalised Mukai conjecture for spherical varieties

Giuliano Gagliardi; Johannes Hofscheier; Heath Pearson

The generalised Mukai conjecture for spherical varieties

Algebraic Geometry 2025-12-30 v2

Authors: Giuliano Gagliardi , Johannes Hofscheier , Heath Pearson

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.

Keywords

toric varieties fano varieties fourier-mukai transform

Cite

@article{arxiv.2502.21155,
  title  = {The generalised Mukai conjecture for spherical varieties},
  author = {Giuliano Gagliardi and Johannes Hofscheier and Heath Pearson},
  journal= {arXiv preprint arXiv:2502.21155},
  year   = {2025}
}

Comments

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

The generalised Mukai conjecture for spherical varieties

Abstract

Keywords

Cite

Comments

Related papers