论文标题
Polyhedra，晶格结构和分数的扩展
Polyhedra, lattice structures, and extensions of semigroups
论文作者
论文摘要
对于任意的有理多面体，我们将其分解为Minkowski汇总，并以此为双重，是相关的半群的自由扩展。对于相应的代数，对这对半群的免费等同于平坦度。我们的主要结果是在此双重设置中进行的：自由扩展的类别始终包含一个初始对象，我们明确描述了该对象。这些对象似乎与日志几何形状中的独特升降机有关。进一步的动机来自相关的复曲面奇异性的变形理论。
For an arbitrary rational polyhedron we consider its decompositions into Minkowski summands and, dual to this, the free extensions of the associated pair of semigroups. Being free for the pair of semigroups is equivalent to flatness for the corresponding algebras. Our main result is phrased in this dual setup: the category of free extensions always contains an initial object, which we describe explicitly. These objects seem to be related to unique liftings in log geometry. Further motivation comes from the deformation theory of the associated toric singularity.
