Semiorthogonal decompositions of derived categories of equivariant coherent sheaves
Semiorthogonal decompositions of derived categories of equivariant coherent sheaves
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等变相干滑轮的派生类别的半正交分解
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发表时间：
2008
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通讯作者：
A. Elagin
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作者：
A. Elagin
设为具有代数群作用的代数变量。假设有一个完整的例外集合，并且这些集合在群的作用下是不变的。构造了-等变相干束的有界派生范畴的半正交分解成等价于的扭曲表示的派生范畴的分量。如果群在特征为0的代数闭域上是有限的或约化的，则给出了派生的等变范畴中的一个完整的例外集合。我们将我们的结果应用于特定的种类，如投影空间、二次曲面、格拉斯曼曲面和德尔佩佐曲面。
Let be an algebraic variety with an action of an algebraic group . Suppose that has a full exceptional collection of sheaves and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of the bounded derived category of -equivariant coherent sheaves on into components that are equivalent to the derived categories of twisted representations of . If the group is finite or reductive over an algebraically closed field of characteristic 0, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmannians and del Pezzo surfaces.