Variations of geometric invariant quotients for pairs, a computational approach
Variations of geometric invariant quotients for pairs, a computational approach
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成对几何不变商的变体，一种计算方法
DOI：
10.1090/proc/13950
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
J. Martínez
中科院分区：
文献类型：
--
作者：
Patricio Gallardo;J. Martínez
研究了由超曲面和超平面构成的对的GIT紧化。我们提供了一个一般的设置来表征所有极化，从而产生不同的GIT商。进一步，我们描述了一个有限的单参数子群集，足以确定任意GIT商的稳定性。我们刻画了所有非稳定和严格半稳定对的极大轨道，以及严格半稳定对的最小闭轨道。我们的构造给出了Fano和Calabi-Yau超曲面的对数光滑对空间的自然紧化。
We study the GIT compactifications of pairs formed by a hypersurface and a hyperplane. We provide a general setting to characterize all polarizations which give rise to different GIT quotients. Furthermore, we describe a finite set of one-parameter subgroups sufficient to determine the stability of any GIT quotient. We characterize all maximal orbits of non stable and strictly semistable pairs, as well as minimal closed orbits of strictly semistable pairs. Our construction gives natural compactifications of the space of log smooth pairs for Fano and Calabi-Yau hypersurfaces.