Mori dream spaces: Theory, algorithms and implementation

森梦空间：理论、算法和实现

• 批准号: 171109699
• 负责人: Professor Dr. Jürgen Hausen
• 金额: --
• 依托单位: Arbeitsbereich Algebra
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/171109699?language=en
• 关键词: Mori; dream; spaces; Theory; algorithms

Mori dream spaces are varieties with a finitely generated Cox ring. Examples are the toric varieties and the Fano varieties. Based on the fact that Mori dream spaces are quotients of affine varieties, one obtains a concrete description of them by means of algebraic-combinatorial data. This generalizes the description of toric varieties in terms of lattice fans and makes Mori dream spaces accessible for computations. We intend to study the geometry of Mori dream spaces in terms of their describing data and to develop and implement algorithms for concrete computations.

Mori型梦空间是一类具有奇异生成的考克斯环的空间。例子是Toric变种和Fano变种。基于Mori梦空间是仿射簇的等价物这一事实，我们利用代数组合数据得到了Mori梦空间的具体描述。这从格扇的角度概括了复曲面簇的描述，并使Mori梦空间可用于计算。我们打算研究的几何形状的森梦空间的描述数据，并开发和实现具体的计算算法。