论文标题
畅通无阻的财产和圆环的商
The well-poised property and torus quotients
论文作者
论文摘要
当从热带品种的点降低且不可还原时，嵌入的品种被据说可以很好地销售。插入良好的品种承认了大量明确构造的牛顿 - 科恩科夫的尸体。 本文旨在研究圆环商下的固定属性。我们的第一个结果指出，准陶里的正常固定品种的GIT商也具有良好的嵌入。作为一个应用程序，我们表明，在Alexeev的嵌入式下，几个Hassett Space，$ \ Overline {M} _ {0，β} $都很好地固定。相反，给定给出的$ t $ - 变量$ x $，带有多面体除数$ \ mathfrak {d} $在固定良好的基础上$ y $上，我们构造了$ x \ subseteq \ subseteq \ mathbb {a a}^n $的嵌入，并在$ y $ y $ y $ y $ y $ y $ y $ \ mathfrak上提供了$ \ \ dis $ $ po的$ po，nme $ poing $ poing $ po n met $ poing。然后，我们表明，任何仿射布置品种都符合指定的标准，概括了Ilten的结果和第二个合理复杂性1品种的作者。使用此结果，我们明确计算了许多$ x $的牛顿 - 科恩科夫锥体，并为相关的复曲面变性提供了标准。我们的最终应用结合了这两个结果，以表明高血压品种具有良好的嵌入。
An embedded variety is said to be well-poised when the associated initial ideal degenerations coming from points of the tropical variety are reduced and irreducible. Varieties with a well-poised embedding admit a large collection of explicitly constructible Newton-Okounkov bodies. This paper aims to study the well-poised property under torus quotients. Our first result states that GIT quotients of normal well-poised varieties by quasi-tori also have well-poised embeddings. As an application, we show that several Hassett spaces, $\overline{M}_{0,β}$, are well-poised under Alexeev's embedding. Conversely, given an affine $T$-variety $X$ with polyhedral divisor $\mathfrak{D}$ on a well-poised base $Y$, we construct an embedding of $X \subseteq \mathbb{A}^N$ and provide conditions on $Y$ and $\mathfrak{D}$ which if met, imply $X$ is well-poised under this embedding. Then we show that any affine arrangement variety meets the specified criteria, generalizing results of Ilten and the second author for rational complexity 1 varieties. Using this result, we explicitly compute many Newton-Okounkov cones of $X$ and provide a criterion for the associated toric degenerations to be normal. Our final application combines these two results to show that hypertoric varieties have well-poised embeddings.
