Frölicher spectral sequence of compact complex manifolds with special Hermitian metrics

Latorre, Adela ; Ugarte, Luis (Universidad de Zaragoza) ; Villacampa, Raquel (Universidad de Zaragoza)

Resumen: In this paper we focus on the interplay between the behaviour of the Frölicher spectral sequence and the existence of special Hermitian metrics on the manifold, such as balanced, SKT or generalized Gauduchon. The study of balanced metrics on nilmanifolds endowed with strongly non-nilpotent complex structures allows us to provide infinite families of compact balanced manifolds with Frölicher spectral sequence not degenerating at the second page. Moreover, this result is extended to non-degeneration at any arbitrary page. Similar results are obtained for the Frölicher spectral sequence of compact generalized Gauduchon manifolds. We also find a compact SKT manifold whose Frölicher spectral sequence does not degenerate at the second page, thus providing a counterexample to a conjecture by Popovici.

Idioma: Inglés

DOI: 10.1007/s10455-024-09972-x

Año: 2024

Publicado en: Annals of Global Analysis and Geometry 66, 3 (2024), 14 [28 pp.]
ISSN: 0232-704X

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)