论文标题
扭曲的霍奇钻石引起了非猎物函数
Twisted Hodge diamonds give rise to non-Fourier-Mukai functors
论文作者
论文摘要
我们应用扭曲的霍奇钻石的计算来构建具有良好行为良好的目标和源空间的无限数量的非峰型函子。为了实现这一目标，我们首先研究了特征形态，以控制倾斜束。然后，我们继续使用嵌入在投影空间中的高空丘脑的扭曲的霍奇钻石来计算这些空间的Hochschild尺寸。这使我们能够计算嵌入到Hochschild共同体中的投影空间中的内核。最后，我们使用上述计算应用了A. Rizzardo，M。van den Bergh和A. Neeman的构造，并验证了构造的函数的确不能成为奇数尺寸Quadrics的傅立叶。使用这种方法，我们证明有大量的Hochschild共同体类可用于这种类型的结构。此外，我们的结果允许应用基于计算机的计算在任意高维度中为任意程度的超曲面构造候选函数。验证这些不是傅立叶木木仍然需要倾斜束。特别是我们证明，每个奇数平滑的二次次数至少有一个非四户函数。
We apply computations of twisted Hodge diamonds to construct an infinite number of non-Fourier-Mukai functors with well behaved target and source spaces. To accomplish this we first study the characteristic morphism in order to control it for tilting bundles. Then we continue by applying twisted Hodge diamonds of hypersurfaces embedded in projective space to compute the Hochschild dimension of these spaces. This allows us to compute the kernel of the embedding into the projective space in Hochschild cohomology. Finally we use the above computations to apply the construction by A. Rizzardo, M. Van den Bergh and A. Neeman of non-Fourier-Mukai functors and verify that the constructed functors indeed cannot be Fourier-Mukai for odd dimensional quadrics. Using this approach we prove that there are a large number of Hochschild cohomology classes that can be used for this type construction. Furthermore, our results allow the application of computer-based calculations to construct candidate functors for arbitrary degree hypersurfaces in arbitrary high dimensions. Verifying that these are not Fourier-Mukai still requires the existence of a tilting bundle. In particular we prove that there is at least one non-Fourier-Mukai functor for every odd dimensional smooth quadric.
