论文标题
热带品种的平行计算，它们的积极部分和热带草个者
Parallel Computation of tropical varieties, their positive part, and tropical Grassmannians
论文作者
论文摘要
在本文中，我们提出了一个可以使用有限对称性的代数品种的热带化的框架。我们计算热带grassmannian tgr $ _0（3,8）$，并表明它完善了Dressian Dr $（3,8）$的$ 15 $维度的骨架，除了$ 23 $的特殊锥体，我们为他们构建了对他们热带线性真实空间的可实现性的明显障碍。此外，我们提出了用于识别属于阳性热带化的最大维度热带锥的算法。这些算法利用了热带品种的对称性，即使阳性热带化不必对称。我们计算阳性Grassmannian Tgr $^+（3,8）$的最大维锥，并将它们与古典Grassmannian Gr $（3,8）$的群集群进行比较。
In this article, we present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of finite symmetries. We compute the tropical Grassmannian TGr$_0(3,8)$, and show that it refines the $15$-dimensional skeleton of the Dressian Dr$(3,8)$ with the exception of $23$ special cones for which we construct explicit obstructions to the realizability of their tropical linear spaces. Moreover, we propose algorithms for identifying maximal-dimensional tropical cones which belong to the positive tropicalization. These algorithms exploit symmetries of the tropical variety even though the positive tropicalization need not be symmetric. We compute the maximal-dimensional cones of the positive Grassmannian TGr$^+(3,8)$ and compare them to the cluster complex of the classical Grassmannian Gr$(3,8)$.
