Derived categories of quadric fibrations and intersections of quadrics
Derived categories of quadric fibrations and intersections of quadrics
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DOI：
10.1016/j.aim.2008.03.007
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发表时间：
2005-10
影响因子：
1.7
通讯作者：
A. Kuznetsov
中科院分区：
文献类型：
--
作者：
A. Kuznetsov
我们构造了二次纤维化上相干滑轮的导出范畴的半正交分解，该二次纤维化由纤维化基部的导出范畴的多个副本和对应于该二次纤维化的克利福德代数偶数部分的束上模的相干滑轮的导出范畴组成，概括了卡普拉诺夫对单个二次曲线的导出范畴的描述。作为一个应用，我们验证非交换代数簇 (P(S2W*),B0)（其中 B0 是 Clifford 代数偶数部分的通用束）与双维罗内嵌入 P(W)→P(S2W) 中的射影空间 P(W) 同调射影对偶。利用同调射影对偶性的性质，我们获得了在任意数量的二次曲面的完全交集上相干滑轮的派生类别的描述。
We construct a semiorthogonal decomposition of the derived category of coherent sheaves on a quadric fibration consisting of several copies of the derived category of the base of the fibration and the derived category of coherent sheaves of modules over the sheaf of even parts of the Clifford algebras on the base corresponding to this quadric fibration generalizing the Kapranov's description of the derived category of a single quadric. As an application we verify that the noncommutative algebraic variety (P(S2W∗),B0), where B0is the universal sheaf of even parts of Clifford algebras, is Homologically Projectively Dual to the projective space P(W) in the double Veronese embedding P(W)→P(S2W). Using the properties of the Homological Projective Duality we obtain a description of the derived category of coherent sheaves on a complete intersection of any number of quadrics.