论奥格雷迪的六维超k {a}勒变异的动机

IF 0.9 Q2 MATHEMATICS Epijournal de Geometrie Algebrique Pub Date : 2022-03-30 DOI:10.46298/epiga.2022.9758

Salvatore Floccari

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引用次数: 5

摘要

证明了在阿贝曲面上半稳定轴的奇异模空间O'Grady型的辛分解得到的六维超k \ {a}的有理Chow动机属于由a $的动机所产生的动机的张量范畴。事实上，我们用表面的理性周氏动机给出了一个公式。因此，Hodge和Tate的猜想对og6型的许多hyper- k \ {a}hler变种都成立。

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On the motive of O'Grady's six dimensional hyper-K\"{a}hler varieties

We prove that the rational Chow motive of a six dimensional hyper-K\"{a}hler variety obtained as symplectic resolution of O'Grady type of a singular moduli space of semistable sheaves on an abelian surface $A$ belongs to the tensor category of motives generated by the motive of $A$. We in fact give a formula for the rational Chow motive of such a variety in terms of that of the surface. As a consequence, the conjectures of Hodge and Tate hold for many hyper-K\"{a}hler varieties of OG6-type.

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