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Algebraic cycles and intersections of a quadric and a cubic
Forum Mathematicum ( IF 0.8 ) Pub Date : 2021-05-01 , DOI: 10.1515/forum-2020-0280
Robert Laterveer 1
Affiliation  

Let Y be a smooth complete intersection of a quadric and a cubic in ℙn{\mathbb{P}^{n}}, with n even. We show that Y has a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. As a consequence, the Chow ring of (powers of) Y displays K3-like behavior. As a by-product of the argument, we also establish a multiplicative Chow–Künneth decomposition for the resolution of singularities of a general nodal cubic hypersurface of even dimension.

中文翻译:

二次和三次的代数循环和交点

令Y为ℙn{\ mathbb {P} ^ {n}}中二次方和三次方的光滑完全交点,其中n为偶数。我们证明,在Shen-Vial的意义上,Y具有可乘的Chow–Künneth分解。结果,Y的Chow环(的幂)显示出类似K3的行为。作为该论证的副产品,我们还建立了乘法Chow-Künneth分解,以解析具有偶数维的一般节点立方超曲面的奇异性。
更新日期:2021-04-29
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