论文标题
热带扩张和图意的品种捆
Tropical expansions and toric variety bundles
论文作者
论文摘要
热带膨胀是其热带化的多面体细分引起的环形嵌入的变性。热带扩展的每个不可还原组成部分都将崩溃的映射降低到原始品种的层。我们研究此图的相对几何形状。我们为地图提供了必要且充分的多面标准，以使其具有感谢您的多种捆绑包的结构，并证明该结构始终存在于代码域内部。我们举例说明这是人们一般希望的最强烈的陈述。此外，我们还提供了一种组合配方，用于构建曲折品种束，作为显式拆分矢量束的纤维git商。我们的证据使系统地使用Artin粉丝作为全球化本地复曲面模型的语言。
A tropical expansion is a degeneration of a toroidal embedding induced by a polyhedral subdivision of its tropicalisation. Each irreducible component of a tropical expansion admits a collapsing map down to a stratum of the original variety. We study the relative geometry of this map. We give a necessary and sufficient polyhedral criterion for the map to have the structure of a toric variety bundle, and prove that this structure always exists over the interior of the codomain. We give examples demonstrating that this is the strongest statement one can hope for in general. In addition, we provide a combinatorial recipe for constructing the toric variety bundle as a fibrewise GIT quotient of an explicit split vector bundle. Our proofs make systematic use of Artin fans as a language for globalising local toric models.
