Generalized hyperbolicity and the geometry of algebraic varieties

广义双曲性和代数簇的几何

• 批准号: RGPIN-2016-05294
• 负责人: Lu, Steven
• 金额: $ 1.6万
• 依托单位: Université du Québec à Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635364
• 关键词: Generalized; hyperbolicity; geometry; algebraic; varieties

We study algebraic varieties from the hyperbolicity perspective. We use Nevanlinna theory, Generalized Ahlfors-Schwarz lemmas, intersection theory and the interplay with and between various differential geometric curvature conditions, etc, for constraining curves and getting positivity (respectively vanishing) of the Kobayashi pseudometric (i.e. (anti)hyperbolicity). We also use modern tools from algebraic geometry in this study, the abundance conjecture in Mori's MMP being a central focus. We have started a revival in this both in complex and in algebraic geometry and aim to continue this promising path by further organized activities and fostering of HQPs.

我们从双曲性的角度研究代数簇。我们使用 Nevanlinna 理论、广义 Ahlfors-Schwarz 引理、相交理论以及各种微分几何曲率条件之间的相互作用等来约束曲线并获得小林伪度量（即（反）双曲性）的正性（分别消失）。我们还在这项研究中使用代数几何的现代工具，Mori 的 MMP 中的丰度猜想是中心焦点。我们已经开始在复数几何和代数几何领域复兴，并旨在通过进一步组织活动和培养 HQP 来继续这条充满希望的道路。