摘要翻译：
我们用两种不同的方法将特征零的代数闭域上的加权射影线关联到正则权系。一种是通过正则权重系统的超曲面奇点定义为商栈，另一种是通过同一正则权重系统的签名定义的。本文的主要结果是：如果一个正则权系是对偶型的，则这两条加权射影线具有等价的相干束的阿贝尔范畴。作为推论，我们可以证明与正则权重系统相关的分次奇点的三角化范畴具有完全的例外集合，这是从同调镜像对称所期望的。本文的主要定理将推广到更一般的定理，推广到正则权系的亏格为零的情形，这将在与Kajiura和Saito的联合论文中给出。由于我们需要更详细地研究正则权系和Deligne-Mumford叠的代数几何知识，作者在本文中写出了一部分结果，可以应用基于Geigle-Lenzing思想的另一个简单证明。
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英文标题：
《Weighted Projective Lines Associated to Regular Systems of Weights of
  Dual Type》
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作者：
Atsushi Takahashi
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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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英文摘要：
  We associate to a regular system of weights a weighted projective line over an algebraically closed field of characteristic zero in two different ways. One is defined as a quotient stack via a hypersurface singularity for a regular system of weights and the other is defined via the signature of the same regular system of weights.   The main result in this paper is that if a regular system of weights is of dual type then these two weighted projective lines have equivalent abelian categories of coherent sheaves. As a corollary, we can show that the triangulated categories of the graded singularity associated to a regular system of weights has a full exceptional collection, which is expected from homological mirror symmetries.   Main theorem of this paper will be generalized to more general one, to the case when a regular system of weights is of genus zero, which will be given in the joint paper with Kajiura and Saito. Since we need more detailed study of regular systems of weights and some knowledge of algebraic geometry of Deligne--Mumford stacks there, the author write a part of the result in this paper to which another simple proof based on the idea by Geigle--Lenzing can be applied.
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PDF链接：
https://arxiv.org/pdf/0711.3907