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The exact algebraic dimension and reduction of complex non-Kähler LVMB manifolds can now be computed directly from the combinatorial nonrationality degree of their underlying toric quasifolds.
Integral Bott--Chern cohomology rings turn out to be completely blind to complex structural differences across generalized Calabi--Eckmann threefolds, requiring an inter-cohomological characteristic map across Dolbeault and singular theories to tell them apart.