Mirror symmetry, affine geometry and Gromov-Hausdorff limits

镜像对称、仿射几何和 Gromov-Hausdorff 极限

• 批准号: 5453439
• 负责人: Professor Dr. Bernd Siebert
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2005
• 资助国家: 德国
• 起止时间: 2004-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5453439?language=en
• 关键词: Mirror; symmetry; affine; geometry; Gromov

Mirror Symmetry is a phenomenon discovered by physicists around 1990. It relates different geometries (symplectic and holomorphic) on pairs of different spaces. This proposal concerns differential-geometric aspects of a joint program with Mark Gross (UCSD) for a comprehensive explanation of this phenomenon by a notion of dual degeneration limits. The program also points to a dictionary of independent interest between symplectic and holomorphic geometry, respectively, on one side and integral affine geometry on the other side.

镜像对称是物理学家在1990年左右发现的一种现象。它涉及不同的几何（辛和全纯）对不同的空间。这个建议涉及微分几何方面的一个联合计划与马克格罗斯（UCSD）的一个全面的解释这种现象的一个概念的双重退化限制。该计划还指出，辛和全纯几何之间的独立利益的字典，分别在一边和积分仿射几何的另一边。