Subharmonicity of direct images and metrics on stable reflexive sheaves

• Applicant: Professor Dr. Mihai Paun, Ph.D.
• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 530472082

The main motivation of this research project is a conjecture due to Campana-Höring-Peternell about the Bogomolov inequality for stable, reflexive Q-sheaves. The solution of this conjecture would lead to the completion of the MMP in the Kähler case in dimension three. Our starting point are the recent important advances in Monge-Ampère theory achieved by the Guo-Phong.Furthermore, we intend to generalize results on subharmonicity of direct image sheaves and systematically investigate concepts for metrics on torsion-free coherent sheaves. For this we use L^2 theory and methods from geometric analysis.

• DFG Programme: Research Grants