The L2 Aeppli-Bott-Chern Hilbert complex

Tom Holt; Riccardo Piovani

doi:10.1016/j.jfa.2024.110596

The L² Aeppli-Bott-Chern Hilbert complex

Tom Holt, Riccardo Piovani

Research output: Contribution to journal › Article › peer-review

Abstract

We analyse the L² Hilbert complexes naturally associated to a non-compact complex manifold, namely the ones which originate from the Dolbeault and the Aeppli-Bott-Chern complexes. In particular we define the L² Aeppli-Bott-Chern Hilbert complex and examine its main properties on general Hermitian manifolds, on complete Kähler manifolds and on Galois coverings of compact complex manifolds. The main results are achieved through the study of self-adjoint extensions of various differential operators whose kernels, on compact Hermitian manifolds, are isomorphic to either Aeppli or Bott-Chern cohomology.

Original language	English
Article number	110596
Journal	Journal of Functional Analysis
Volume	287
Issue number	9
Early online date	22 Jul 2024
DOIs	https://doi.org/10.1016/j.jfa.2024.110596
Publication status	E-pub ahead of print - 22 Jul 2024
Externally published	Yes

Data Availability Statement

No data was used for the research described in the article.

Funding

The second author is partially supported by GNSAGA of INdAM and by University of Parma through the action Bando di Ateneo 2023 per la ricerca.

Funders	Funder number
GNSAGA
INdAM
Università degli Studi di Parma

Keywords

Complete Kähler metrics
Complex manifolds
Galois coverings
Spectral gap

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2024.110596Licence: CC BY

Cite this

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AB - We analyse the L2 Hilbert complexes naturally associated to a non-compact complex manifold, namely the ones which originate from the Dolbeault and the Aeppli-Bott-Chern complexes. In particular we define the L2 Aeppli-Bott-Chern Hilbert complex and examine its main properties on general Hermitian manifolds, on complete Kähler manifolds and on Galois coverings of compact complex manifolds. The main results are achieved through the study of self-adjoint extensions of various differential operators whose kernels, on compact Hermitian manifolds, are isomorphic to either Aeppli or Bott-Chern cohomology.

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