摘要翻译：
本文简要介绍并回顾了近十年来在理解主极化阿贝尔变体模空间A_g及其紧致性的几何方面所取得的进展。调查的主题包括：紧凑；双形几何：nef与有效锥，正则模型；同调、Chow环与交集理论；和模空间的子变体。我们还讨论了一些尚待解决的问题和可能的进一步发展方向。这是2005年夏季代数几何学院演讲的扩展和更新版本
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英文标题：
《Geometry of A_g and Its Compactifications》
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作者：
Samuel Grushevsky
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最新提交年份：
2010
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  In this survey we give a brief introduction to, and review the progress made in the last decade in understanding the geometry of the moduli spaces A_g of principally polarized abelian varieties and its compactifications. Topics surveyed include: compactifications; birational geometry: nef and effective cones, canonical models; homology, Chow rings and intersection theory; and subvarieties of moduli spaces. We also discuss some open problems and possible further directions. This is an expanded and updated version of the talk given at the 2005 Summer Institute for Algebraic Geometry
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PDF链接：
https://arxiv.org/pdf/0711.0094