Convex projective manifolds with a cusp of any non-diagonalizable type

TL;DR

This paper extends techniques to demonstrate the existence of all non-diagonalizable convex projective cusp types across all dimensions, broadening understanding of geometric structures beyond hyperbolic cases.

Contribution

It proves the existence of all non-diagonalizable convex projective cusp types in every dimension, except the diagonalizable (type n), using extended methods.

Findings

Existence of all non-diagonalizable cusp types in all dimensions.

Extension of techniques from previous work to higher dimensions.

Exclusion of diagonalizable (type n) cusps from the existence results.

Abstract

Recent work of Ballas, Cooper, and Leitner identifies $(n+1)$ types of $n$-dimensional convex projective cusps, one of which is the standard hyperbolic cusp. Work of Ballas-Marquis, and Ballas-Danciger-Lee give examples of these exotic (non-hyperbolic) type cusps in dimension $3$. Here an extension of the techniques of Ballas-Marquis shows the existence of all cusp types in all dimensions, except diagonalizable (type $n$).