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arXiv · 2607.26786

Invariant forms compute the Dolbeault cohomology of complex nilmanifolds

Keizo Hasegawa·Lorenzo Sillari·Adriano Tomassini
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Abstract

We prove that the inclusion of left-invariant forms into the Dolbeault complex of a compact nilmanifold $M$ endowed with a left-invariant complex structure $J$ induces an isomorphism in cohomology in every bidegree, settling a long-standing conjecture. As consequences, we show that small deformations of $J$ are still invariant, as conjectured by Hasegawa. We also prove that Bott--Chern, Aeppli, and Fr\"olicher invariants are computed by invariant forms and are independent of the lattice, settling a conjecture of Angella on Bott--Chern cohomology.

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Keizo Hasegawa, Lorenzo Sillari, Adriano Tomassini. 2026-07-29. Invariant forms compute the Dolbeault cohomology of complex nilmanifolds. https://arxiv.org/abs/2607.26786

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