Work

Vanishing theorem for tame harmonic bundles via L 2 -cohomology

Year: 2024

Type: article

Abstract: Using $L^2$ -methods, we prove a vanishing theorem for tame harmonic bundles over quasi-compact Kähler manifolds in a very general setting. As a special case, we give a completely new proof of the Kodaira-type vanishing theorems for Higgs bundles due to Arapura. To prove our vanishing theorem, we construct a fine resolution of the Dolbeault complex for tame harmonic bundles via the complex of sheaves of $L^2$ -forms, and we establish the Hörmander $L^2$ -estimate and solve $(\bar {\partial }_E+\theta )$ -equations for Higgs bundles $(E,\theta )$ .

Source: Compositio Mathematica

DOI: 10.1112/s0010437x24007504

Authors: Ya Deng, Feng Hao

Institutions: Centre National de la Recherche Scientifique, Institut Élie Cartan de Lorraine, Université de Lorraine, Shandong University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Agence Nationale de la Recherche, Universite Angers

Award: Kähler manifolds with non-positive curvature: families and special subvarieties