基于几何热带化的曲面隐式化
Implicitization of surfaces via geometric tropicalization
摘要：
在本文中，我们进一步发展的几何热带化理论，由于黑客，龙骨和Tevelev和我们描述的热带方法的表面隐式化。更确切地说，我们丰富了这一理论与热带多重性的组合公式在任意维度的正则点，我们证明了一个猜想的Sturmfels和Tevelev关于充分的组合条件，通过几何热带化计算热带品种。利用这两个结果，我们扩展了以前的工作Sturmfels，Tevelev和Yu的热带隐含的通用表面，我们提供的方法接近非通用的情况下。
英文摘要：
In this paper we further develop the theory of geometric tropicalization due to Hacking, Keel and Tevelev and we describe tropical methods for implicitization of surfaces. More precisely, we enrich this theory with a combinatorial formula for tropical multiplicities of regular points in arbitrary dimension and we prove a conjecture of Sturmfels and Tevelev regarding sufficient combinatorial conditions to compute tropical varieties via geometric tropicalization. Using these two results, we extend previous work of Sturmfels, Tevelev and Yu for tropical implicitization of generic surfaces, and we provide methods for approaching the non-generic cases.
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