论文标题
Bitangents到热带四分之一曲线的组合和真实升降机
Combinatorics and real lifts of bitangents to tropical quartic curves
论文作者
论文摘要
在代数封闭的字段上，平滑代数平面四分之一具有28个BITANGENT线。他们的热带对应物通常具有无限的许多比尼格。它们分为七个等价类别，每个线性系统都与热带四分之一的有效热带theta特征相关联。我们显示这样的类确定热地凸集，并将此类对象的完整组合分类分为41种类型（直至对称）。 给定类别的出现由组合类型和输入热带平面四分之一的度量结构确定。我们使用此结果来提供明确的标志规则，以获得每个热带bitangent类的真实升降机，并确认每个人都有零或四个真实的升降机，如Len和第二作者先前猜想。此外，这种真正的升降机总是完全实现的。
Smooth algebraic plane quartics over algebraically closed fields have 28 bitangent lines. Their tropical counterparts often have infinitely many bitangents. They are grouped into seven equivalence classes, one for each linear system associated to an effective tropical theta characteristic on the tropical quartic. We show such classes determine tropically convex sets and provide a complete combinatorial classification of such objects into 41 types (up to symmetry). The occurrence of a given class is determined by both the combinatorial type and the metric structure of the input tropical plane quartic. We use this result to provide explicit sign-rules to obtain real lifts for each tropical bitangent class, and confirm that each one has either zero or exactly four real lifts, as previously conjectured by Len and the second author. Furthermore, such real lifts are always totally-real.
