论文标题
K3表面和双立方四倍的Abelian动机
K3 surfaces and cubic fourfolds with Abelian motive
论文作者
论文摘要
我们表明，具有代数的2循环的晶格大于19的立方四倍，其中19位具有Abelian和有限的维度（在Kimura的意义上）Chow Motive。这也意味着相关Hyperkahler品种动机的Abelianity和有限维度，例如Fano种类的品种和LLSVS 8倍。类似的说法使我们能够表明LSV 10倍无穷大的动机以及其他与相关K3表面的Cutic Fourds的扭曲中间Jacobian纤维相关的Hyperkahler 10倍。之后，从某些4维家族的K3表面开始，我们构建了两个Fano品种的家族，它们的Chow动机是有限的尺寸。第一家族的品种是一些二次表面振动，并包含K3表面的有限尺寸先验动机。第二个家庭的品种是奇异的立方四倍，它们的动机是Schur-Finite和Abelian在Voevodsky的三角动机类别中。
We show that cubic fourfolds with lattice of algebraic 2-cycles of rank greater than 19 have abelian and finite dimensional (in the sense of Kimura) Chow motive. This also implies Abelianity and finite dimensionality of the motive of related hyperKahler varieties, such as the Fano variety of lines and the LLSvS 8fold. A similar remark allows us to show the Abelianity of the motive of an infinity of LSV 10folds, and of other hyperKahler 10folds associated to the twisted intermediate Jacobian fibration of cubic fourfolds with an associated K3 surface. After that, starting from certain 4-dimensional families of K3 surfaces, we construct two families of Fano varieties whose Chow motive is finite dimensional. Varieties from the first family are some quadric surface fibrations, and contain the finite dimensional transcendental motive of a K3 surface. Varieties from the second family are singular cubic fourfolds, and their motives are Schur-finite and Abelian in Voevodsky's triangulated category of motives.
