标题： 辛拓扑几何中单调爆破的结构以及McDuff的一个问题 显示英文标题

标题： The structure of monotone blow-ups in symplectic toric geometry and a question of McDuff

摘要： 单调多面体，也称为光滑反射多面体，是与单调辛环面流形和Gorenstein Fano环面代数簇相关的多面体。 我们首先证明，唯一允许在顶点处进行爆破的单调多面体是单形以及其中二维余维爆破的结果（这是对Bonavero于2002年结果的多面体版本）。 然后我们证明，$n$-单形在面上进行不相交爆破当且仅当这些面不相交且它们的维数之和为$n-1$或$n-2$。 这些结果回答了Dusa McDuff在2011年提出的问题。 显示英文摘要

摘要： Monotone polytopes, also known as smooth reflexive polytopes, are the polytopes associated to monotone symplectic toric manifolds and Gorenstein Fano toric varieties. We first show that the only monotone polytopes admitting blow-ups at vertices are the simplex and the result of a codimension-two blow-up in it (this is the polyhedral version of a result of Bonavero from 2002). Then we show that the $n$-simplex admits disjoint blow-ups at faces if and only if the faces are disjoint and have dimensions adding up to $n-1$ or $n-2$. These results answer a question posed by Dusa McDuff in 2011.