Torsion orders of complete intersections
Torsion orders of complete intersections
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DOI：
10.2140/ant.2017.11.1779
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发表时间：
2016-05
影响因子：
1.3
通讯作者：
A. Chatzistamatiou;M. Levine
中科院分区：
文献类型：
--
作者：
A. Chatzistamatiou;M. Levine
根据Roitman的一个经典结果，一个充分小度的完全交X允许对角线的有理分解。这意味着对角线乘以一个正整数N的倍数，当被看作周群中的一个循环时，在X\times D\cup F\times X$中有支持，对于某个除数D$和一个有限的闭点集F$。最小的这样的$N$被称为挠序。我们研究了Voisin，Colliot-Th 'el' ene和Pirutka的特殊化方法下的挠序的下界。给出了一般的有点完全交和无点完全交的下界。此外，我们使用Koll\'ar和Totaro的方法来显示非常一般的完全相交的下界。
By a classical result of Roitman, a complete intersection $X$ of sufficiently small degree admits a rational decomposition of the diagonal. This means that some multiple of the diagonal by a positive integer $N$, when viewed as a cycle in the Chow group, has support in $X\times D\cup F\times X$, for some divisor $D$ and a finite set of closed points $F$. The minimal such $N$ is called the torsion order. We study lower bounds for the torsion order following the specialization method of Voisin, Colliot-Th\'el\`ene and Pirutka. We give a lower bound for the generic complete intersection with and without point. Moreover, we use methods of Koll\'ar and Totaro to show lower bounds for the very general complete intersection.