论文标题
地图到曲曲面的品种和复曲面变性
Maps to toric varieties and toric degenerations
论文作者
论文摘要
我们研究并构建图形的图片。在此过程中，我们将圆环的嵌入概括为非注射案例。此外，我们将Cox的旋转品种的构造类似于T. Kajiwara之后的非正常情况。 本文的主要重点是将特殊纤维不必要的福利型福利的家族（适当的）植物应用。我们对I. Dolgachev和K. K.的问题给出了负面答案，即是否可以通过投影构建复的变性。在复数的古典拓扑中，我们恢复了整体系统的替代构造，就像Harada-Kaveh M. Harada和K. Kaveh所做的那样。使用变形缩回的“可集成系统，曲折的变性和Okounkov Bodie”。特别是，我们有一个瞬间图的类似物，从一个多样性地承认曲折的变性到其牛顿 - 科恩科夫·多层。
We study and construct maps to toric varieties. In the process, we generalize torus embeddings to the non-projective case. Moreover, we give an analog of Cox's construction of toric varieties as GIT quotients of affine spaces for the non-normal case after T. Kajiwara. The main focus of the paper is an application to toric degenerations, (proper) families whose special fibers are not-necessarily-normal toric varieties. We give a negative answer to a question of I. Dolgachev and K. Kaveh as to whether a toric degeneration can be constructed as a degeneration by projection. In the classical topology over the complex numbers, we recover an alternative construction of integral systems as was done by Harada--Kaveh in M. Harada and K. Kaveh. "Integrable systems, toric degenerations and okounkov bodie" using a deformation retract. In particular, we have an analogue of a moment map from a variety admitting a toric degeneration to its Newton--Okounkov polytope.
