$\mathbb{H}_{2n+1}$-structures on odd dimensional projective spaces

TL;DR

This paper demonstrates that the Heisenberg group $ ext{H}_{2n+1}$ can be embedded in infinitely many inequivalent ways into projective spaces, extending classical results to non-commutative algebraic groups.

Contribution

It establishes the existence of infinitely many inequivalent equivariant compactifications of the Heisenberg group into projective spaces for all dimensions.

Findings

Infinite inequivalent equivariant compactifications of $ ext{H}_{2n+1}$ into $ ext{P}^{2n+1}$ for all $n",

Extension of classical results to non-commutative algebraic groups.

Abstract

We prove that the Heisenberg group $\h_{2n+1}$ admits infinitely many inequivalent equivariant compactifications into $\mathbb{P}^{2n+1}$ for all $n\geq 1$. This result provides an analog of Hassett-Tschinkel's classical result beyond commutative algebraic groups.