Complete moduli in the presence of semiabelian group action
Complete moduli in the presence of semiabelian group action
复制标题
存在半阿贝尔群作用时的完全模
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
V. Alexeev
中科院分区：
文献类型：
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作者：
V. Alexeev
证明了由具有半交换群作用的射影簇P和满足几个简单条件的充裕卡地亚因子构成的对(P，Θ)的模空间的存在性，并刻画了它的结构。这个模空间的每个连通分支都是真的。包含射影环面簇的分量由几个多面体的构形来描述。其中最主要的是次要多面体。另一方面，包含主要极化的阿贝尔变种的分量提供了Ag的模紧化。这种压实作用的主要不可约分量由次生多面体的无限周期模拟来描述，并与第二次Voronoi分解的Ag的环状压实相吻合。
I prove the existence, and describe the structure, of moduli space of pairs (P, Θ) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every connected component of this moduli space is proper. A component containing a projective toric variety is described by a configuration of several polytopes. the main one of which is the secondary polytope. On the other hand, the component containing a principally polarized abelian variety provides a moduli compactification of A g . The main irreducible component of this compactification is described by an infinite periodic analog of the secondary polytope and coincides with the toroidal compactification of A g for the second Voronoi decomposition.