共查询到4条相似文献,搜索用时 15 毫秒
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Robert Laterveer 《数学学报(英文版)》2017,33(7):887-898
This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family. 相似文献
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Ivan Bazhov 《Journal of Pure and Applied Algebra》2019,223(6):2530-2542
We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold. 相似文献
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《Mathematische Nachrichten》2018,291(7):1088-1113
Let X be a hyperkähler variety with an anti‐symplectic involution ι. According to Beauville's conjectural “splitting property”, the Chow groups of X should split in a finite number of pieces such that the Chow ring has a bigrading. The Bloch–Beilinson conjectures predict how ι should act on certain of these pieces of the Chow groups. We verify part of this conjecture for a 19‐dimensional family of hyperkähler sixfolds that are “double EPW cubes” (in the sense of Iliev–Kapustka–Kapustka–Ranestad). This has interesting consequences for the Chow ring of the quotient , which is an “EPW cube” (in the sense of Iliev–Kapustka–Kapustka–Ranestad). 相似文献