Seminar series
Date
Wed, 03 Jun 2026
15:00
15:00
Location
C6
Speaker
Heath Pearson
Organisation
Nottingham
This is a case study in approaching algebraic-geometric questions by first solving them in a combinatorially tractable class, and then generalising the findings through a sequence of increasingly general classes. The end goal is a proof of the general case. We call this process a ``decombinatorialisation''.
Executing such a process remains a lofty goal, and here we present only the first steps of what could be considered a decombinatorialisation. In this talk, we explore the Mukai conjecture on the characterisation of powers of projective spaces among Fano varieties. We will see how over time, generalisations of its proof in the case of toric Fano varieties have emerged.
In this setting we will explore two possible decombinatorialisations: via the class of spherical Fano varieties, and via a class of Fanos embedded into toric varieties via the Cox ring.