Algorithmic tropical intersection theory on moduli spaces

模空间的算法热带相交理论

• 批准号: 170992108
• 负责人: Professor Dr. Andreas Gathmann
• 金额: --
• 依托单位: Mathematics Institute
• 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 2013-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/170992108?language=en
• 关键词: Algorithmic; tropical; intersection; theory; moduli

The new research field of tropical geometry has recently led to considerable progress in algebraic geometry and particularly enumerative geometry. With the help of tropical geometry, many algebraic or geometric questions can be reduced to combinatorial problems concerning graphs or polyhedral complexes. However, the structure of these combinatorial problems is involved, which makes the theoretical as well as practical use of these results complicated. Therefore, we would like to develop resp. implement algorithms for several of these problems which are of particular interest. Thus, we do not only want to gain new results in tropical and hence algebraic geometry, but we also want to simplify the application of tropical geometry.

热带几何这一新的研究领域最近使代数几何特别是枚举几何取得了相当大的进展。借助于热带几何，许多代数或几何问题可以归结为有关图或多面体复形的组合问题。然而，这些组合问题的结构，这使得这些结果的理论和实际应用复杂。因此，我们希望开发RESP。为这些特别感兴趣的问题中的几个实现算法。因此，我们不仅希望在热带几何和代数几何中获得新的结果，而且还希望简化热带几何的应用。