基于系统发生群模型的局部描述
Local description of phylogenetic group-based models
摘要：
受遗传学的启发，我们的目标是获得一个方程组，该方程组定义了一个包含生物学意义点的开集上的系统发育多样性。在本文中，我们认为通过基于组的模型定义的系统发育的品种。对于任何有限阿贝尔群$G$，我们提供了一个明确的结构$codim X$系统发育不变量（多项式方程）的程度最多$|G|$，定义品种$X$上的Zurski开集$U$。当$G$是Kimura 3-参数模型的组时，集合$U$包含所有生物学上有意义的点。特别地，我们的主要结果证实了第三作者的一个猜想，并在集合$U$上，证实了Bernd Sturmfels和Seth Sullivant的几个猜想。
英文摘要：
Motivated by phylogenetics, our aim is to obtain a system of equations that define a phylogenetic variety on an open set containing the biologically meaningful points. In this paper we consider phylogenetic varieties defined via group-based models. For any finite abelian group $G$, we provide an explicit construction of $codim X$ phylogenetic invariants (polynomial equations) of degree at most $|G|$ that define the variety $X$ on a Zariski open set $U$. The set $U$ contains all biologically meaningful points when $G$ is the group of the Kimura 3-parameter model. In particular, our main result confirms a conjecture by the third author and, on the set $U$, a couple of conjectures by Bernd Sturmfels and Seth Sullivant.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
