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arXiv · 2502.01447

Higher-Degree Holomorphic Contact Structures

Hisashi Kasuya·Dan Popovici·Luis Ugarte
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Abstract

We introduce the classes of holomorphic $p$-contact manifolds and holomorphic $s$-symplectic manifolds that generalise the classical holomorphic contact and holomorphic symplectic structures. After observing their basic properties and exhibiting a wide range of examples, we give two types of general conceptual results involving the former class of manifolds: structure theorems and unobstructedness theorems. The latter type generalises to our context the classical Bogomolov-Tian-Todorov theorem for a type of small deformations of complex structures that generalise the small essential deformations previously introduced for the Iwasawa manifold and for Calabi-Yau page-$1$-$\partial\bar\partial$-manifolds.

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Hisashi Kasuya, Dan Popovici, Luis Ugarte. 2025-02-03. Higher-Degree Holomorphic Contact Structures. https://arxiv.org/abs/2502.01447

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