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arXiv · 2208.01074

A ddc-type condition beyond the K\"ahler realm

Jonas Stelzig·Scott O. Wilson
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Abstract

This paper introduces a generalization of the ddc-condition for complex manifolds. Like the dd^c-condition, it admits a diverse collection of characterizations, and is hereditary under various geometric constructions. Most notably, it is an open property with respect to small deformations. The condition is satisfied by a wide range of complex manifolds including all compact complex surfaces, and all compact Vaisman manifolds. We show there are computable invariants of a real homotopy type which in many cases prohibit it from containing any complex manifold satisfying such ddc-type conditions in low degrees. This gives rise to numerous examples of almost complex manifolds which cannot be homotopy equivalent to any of these complex manifolds.

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BibTeXRIS

Jonas Stelzig, Scott O. Wilson. 2022-08-01. A ddc-type condition beyond the K\"ahler realm. https://arxiv.org/abs/2208.01074

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