摘要翻译：
D.Abramovich,K.Karu,K.Matsuki和J.Wlodarczyk的toroidalization猜想提出了一个问题，即在特征为零的代数闭域上，非奇异簇的任何给定态射是否可以被修改为toroidalization态射。根据Dale Cutkosky的建议，我们定义了\emph{局部超环}态射的概念，并提出了是否可以将任何局部超环态射修正为超环态射的问题。本文对任意变体与曲面之间的态射作了肯定的回答。
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英文标题：
《Toroidalization of Locally Toroidal Morphisms from N-folds to Surfaces》
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作者：
Krishna Hanumanthu
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最新提交年份：
2008
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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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一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
  The toroidalization conjecture of D. Abramovich, K. Karu, K. Matsuki, and J. Wlodarczyk asks whether any given morphism of nonsingular varieties over an algebraically closed field of characteristic zero can be modified into a toroidal morphism. Following a suggestion by Dale Cutkosky, we define the notion of \emph{locally toroidal} morphisms and ask whether any locally toroidal morphism can be modified into a toroidal morphism. In this paper, we answer the question in the affirmative when the morphism is between any arbitrary variety and a surface.
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PDF链接：
https://arxiv.org/pdf/0803.4210