AI 中文总结
本文研究上除子的有效边界表达式多面体，建立其结构与图论描述，计算多类除子的多面体并将其与生成树、旅行商问题等多面体关联，还得到子图消除多面体的分解及共形块除子多面体的相关性质。
AI 中文摘要
对于上的一个除子，我们引入其有效边界表达式的多面体。我们在遗忘标记点的遗忘映射下建立这些多面体的结构性质，并给出等价的图论描述。我们计算了几类除子的这类多面体：对于psi类及其经遗忘映射的拉回，证明这些多面体是幺模单形；对于对数典范类及其经psi类的修正，证明对应多面体的非负部分恢复了生成树多面体和对称旅行商问题的子图消除（Held--Karp松弛）多面体；作为应用，我们得到子图消除多面体的类单形的Minkowski分解；最后，对于对称一级共形块除子，证明其定义不等式是局部Turán界，且0/1点是平衡Turán图，此外当p=2且p=n/2时，这些多面体恢复了完美匹配和分数完美匹配多面体。
英文摘要
For a divisor on $\overline{M}_{0,n}$, we introduce the polytope of its effective boundary expressions. We establish structural properties of these polytopes under the forgetful maps of $\overline{M}_{0,n}$ forgetting marked points, and give equivalent graph-theoretic descriptions. We compute these polytopes for several families of divisors. For psi-classes and their pullbacks by forgetful maps, we show that the polytopes are unimodular simplices. For the log-canonical class and its modifications by psi-classes, we prove that the nonnegative parts of the corresponding polytopes recover spanning forest polytopes and the subtour elimination (Held--Karp relaxation) polytope of the symmetric traveling salesman problem. As an application, we obtain a Minkowski-like decomposition of the subtour elimination polytope into simplices. Finally, for symmetric level-one $\mathfrak{sl}_p$ conformal block divisors, we show that the defining inequalities are local Turán bounds and the $0/1$-points are balanced Turán graphs. Moreover, for $p=2$ and $p=n/2$, these polytopes recover the perfect matching and fractional perfect matching polytopes.
Comments52 pages, 10 figures. Comments welcome!
