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This work proves infinitely many compactifications of the Heisenberg group in projective spaces, suggesting new geometric structures.
We prove that the Heisenberg group admits infinitely many inequivalent equivariant compactifications into for all . This result provides a non‐commutative analog of Hassett–Tschinkel's classical result, which shows that there exist infinitely many inequivalent equivariant compactifications of vector groups into projective spaces of dimension at least 6.
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Ding et al. (2026) studied this question.
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