论文标题
二次富集的热带交集
Quadratically Enriched Tropical Intersections
论文作者
论文摘要
使用热带几何形状可以将枚举几何形状的问题转化为结合问题。因此，热带几何形状是复杂和实数的枚举几何形状的强大工具。 $ \ mathbb {a}^1 $ - homotophy理论允许丰富经典的枚举几何问题并通过任意领域获得答案。在结果区域中，$ \ mathbb {a}^1 $增强的几何形状，这些问题的答案生存在基础场$ k $的Grothendieck-Witt戒指中。在本文中，我们通过显示Bézout的定理和概括（即Bernstein-Kushnirenko定理）中使用的热带方法，用于在$ \ operatatoRatorname {gw}（k）$中富集的热带超曲面。
Using tropical geometry one can translate problems in enumerative geometry to combinatorial problems. Thus tropical geometry is a powerful tool in enumerative geometry over the complex and real numbers. Results from $\mathbb{A}^1$-homotopy theory allow to enrich classical enumerative geometry questions and get answers over an arbitrary field. In the resulting area, $\mathbb{A}^1$-enumerative geometry, the answer to these questions lives in the Grothendieck-Witt ring of the base field $k$. In this paper, we use tropical methods in this enriched set up by showing Bézout's theorem and a generalization, namely the Bernstein-Kushnirenko theorem, for tropical hypersurfaces enriched in $\operatorname{GW}(k)$.
