Subharmonicity of direct images and metrics on stable reflexive sheaves

稳定反射滑轮上直接图像和度量的次谐波

• 批准号: 530472082
• 负责人: Professor Dr. Mihai Paun, Ph.D.
• 金额: --
• 依托单位: Lehrstuhl Mathematik VIII - Algebraische Geometrie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/530472082?language=en
• 关键词: Subharmonicity; direct; images; metrics; stable

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.

本研究项目的主要动机是由于Campana-Höring-Peternell关于稳定自反q -轴的Bogomolov不等式的猜想。这个猜想的解决将导致在三维Kähler情况下的MMP的完成。我们的出发点是最近在蒙日-安普瑞理论取得的重要进展的郭峰。此外，我们打算推广直接像轴的次谐波结果，并系统地研究无扭相干轴的度量概念。为此，我们使用L^2理论和几何分析中的方法。