Graded rings and equivariant sheaves on toric varieties
Graded rings and equivariant sheaves on toric varieties
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复曲面品种上的分级环和等变滑轮
DOI：
10.1002/mana.200310130
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发表时间：
2002
影响因子：
1
通讯作者：
Markus Perling
中科院分区：
文献类型：
--
作者：
Markus Perling
在这篇笔记中，我们推导了一个描述环型变异上的等变捆的形式。这种形式是Klyachko对应的推广，Klyachko指出，环上的等变向量束等价于向量空间的某些过滤集。我们从分级环理论的角度系统地构建了这一理论，从而澄清了Kaneyama和Klyachko的早期构造。我们还将该形式主义与环型Cox齐次坐标环上的细阶模理论联系起来。作为一个应用，我们构造了环面上二阶等变向量束的最小分辨率。（©2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim）
In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are equivalent to certain sets of filtrations of vector spaces. We systematically construct the theory from the point of view of graded ring theory and this way we clarify earlier constructions of Kaneyama and Klyachko. We also connect the formalism to the theory of fine‐graded modules over Cox' homogeneous coordinate ring of a toric variety. As an application we construct minimal resolutions of equivariant vector bundles of rank two on toric surfaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)