The $L^2$ Aeppli-Bott-Chern Hilbert complex

Tom Holt; Riccardo Piovani

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arXiv · 2310.08993

The $L^2$ Aeppli-Bott-Chern Hilbert complex

Tom Holt·Riccardo Piovani

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Abstract

We analyse the $L^2$ 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 $L^2$ Aeppli-Bott-Chern Hilbert complex and examine its main properties on general Hermitian manifolds, on complete K\"ahler 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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Tom Holt, Riccardo Piovani. 2023-10-13. The $L^2$ Aeppli-Bott-Chern Hilbert complex. https://arxiv.org/abs/2310.08993

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