与立方四面体相关的 K3 表面

Claudio Pedrini
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引用次数: 0

摘要

假设是一个光滑的三次方四面体。一个众所周知的猜想断言,当且仅当存在一个霍奇理论上关联的 K3 曲面时,该曲面是合理的。该曲面可以通过两种不同的方式与之关联。如果有一个等价范畴,其中是库兹涅佐夫分量,并且是一个布劳尔类,或者如果 K3 曲面的超越动机和(扭曲的)超越动机之间存在同构。在本论文中,我们考虑了具有有限自形群的立方四折体族,并描述了存在上述意义之一的关联 K3 曲面的情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
K3 surfaces associated to a cubic fourfold
Let be a smooth cubic fourfold. A well known conjecture asserts that is rational if and only if there a Hodge theoretically associated K3 surface . The surface can be associated to in two other different ways. If there is an equivalence of categories where is the Kuznetsov component of and is a Brauer class, or if there is an isomorphism between the transcendental motive and the (twisted ) transcendental motive of a K3 surface . In this note we consider families of cubic fourfolds with a finite group of automorphisms and describe the cases where there is an associated K3 surface in one of the above senses.
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