论文标题
不对称的热带距离和功率图
Asymmetric tropical distances and power diagrams
论文作者
论文摘要
我们研究了无限点集的不对称热带距离函数的Voronoi图。这些事实比由标准的热带距离引起的热带伏诺曲（Tropical Voronoi图）要好得多，这是对称的。特别是，我们表明，不对称的热带伏诺曲图可以看作是真实Puiseux系列领域的功率图的热带化。然后，我们的结果将应用于有理晶格和劳伦（Laurent）单一模块。
We investigate the Voronoi diagrams with respect to an asymmetric tropical distance function, also for infinite point sets. These turn out to be much better behaved than the tropical Voronoi diagrams arising from the standard tropical distance, which is symmetric. In particular, we show that the asymmetric tropical Voronoi diagrams may be seen as tropicalizations of power diagrams over fields of real Puiseux series. Our results are then applied to rational lattices and Laurent monomial modules.
