Holomorphic $p$-Contact and $s$-Symplectic Line Bundles

Fuente: arXiv
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Autori principali: Broder, Kyle, Popovici, Dan
Natura: Preprint
Pubblicazione: 2025
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author Broder, Kyle
Popovici, Dan
author_facet Broder, Kyle
Popovici, Dan
contents We generalise the notions of scalar-valued holomorphic $p$-contact and $s$-symplectic structures introduced recently on compact complex manifolds by the second-named author jointly with H. Kasuya and L. Ugarte to their analogues with values in a holomorphic line bundle. We then study the resulting holomorphic $p$-contact and $s$-symplectic manifolds which, unlike their scalar counterparts that are never Kähler, can even be projective. In particular, we investigate the (lack of) positivity properties of the canonical bundle of these manifolds when it is given a possibly singular Hermitian fibre metric. One of the tools used is a very recent regularisation result for $m$-psh functions obtained jointly by S. Dinew and the second-named author.
format Preprint
id arxiv_https___arxiv_org_abs_2511_23139
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Holomorphic $p$-Contact and $s$-Symplectic Line Bundles
Broder, Kyle
Popovici, Dan
Differential Geometry
Algebraic Geometry
Complex Variables
We generalise the notions of scalar-valued holomorphic $p$-contact and $s$-symplectic structures introduced recently on compact complex manifolds by the second-named author jointly with H. Kasuya and L. Ugarte to their analogues with values in a holomorphic line bundle. We then study the resulting holomorphic $p$-contact and $s$-symplectic manifolds which, unlike their scalar counterparts that are never Kähler, can even be projective. In particular, we investigate the (lack of) positivity properties of the canonical bundle of these manifolds when it is given a possibly singular Hermitian fibre metric. One of the tools used is a very recent regularisation result for $m$-psh functions obtained jointly by S. Dinew and the second-named author.
title Holomorphic $p$-Contact and $s$-Symplectic Line Bundles
topic Differential Geometry
Algebraic Geometry
Complex Variables
url https://arxiv.org/abs/2511.23139