In the abelian case compact abelian Lie groups are unique up to diffeomorphism i.e. $(S^1)^n$.
How about the complex case? Are complex tori unique up to holomorphism i.e $(T)^n$ where $T=S^1\times S^1$?
2026-03-26 06:32:53.1774506773
Uniqueness of complex tori
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No. There is a one-dimensional moduli of elliptic curves, for example.