Triangulations and Severi varieties
Fr\'ed\'eric Chapoton (ICJ), Laurent Manivel (IF)

TL;DR
This paper explores minimal vertex triangulations of projective planes over Hurwitz algebras, linking face counts to automorphism group representations of Severi varieties, and proposes a geometric complex as a triangulation analogue.
Contribution
It introduces a novel approach connecting triangulations with automorphism representations of Severi varieties, providing a geometric framework for these structures.
Findings
Face counts match dimensions of automorphism group representations
Constructed a complex representing the triangulation structure
Proposed a geometric analogue of triangulations for Severi varieties
Abstract
We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations.
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