Unirational threefolds with no universal codimension $$2$$2 cycle
Unirational threefolds with no universal codimension $$2$$2 cycle
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DOI：
10.1007/s00222-014-0551-y
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发表时间：
2013-12
影响因子：
3.1
通讯作者：
C. Voisin
中科院分区：
文献类型：
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作者：
C. Voisin
本文证明了一般的四次双结点立体不允许对角的Chow理论分解（或等价地有一个非平凡的泛群），如果我们用“上同调”代替“Chow理论”，同样成立。特别是，它不是稳定理性的。我们还推出，一般的四次双固体与七个节点不允许一个通用的余维圈参数化的中间雅可比，甚至不允许一个参数化的合理连接纤维的雅可比族的周期。这最终意味着它的第三个非分歧上同调群不是泛平凡的。
We prove that the general quartic double solid withnodes does not admit a Chow theoretic decomposition of the diagonal, (or equivalently has a nontrivial universalgroup,) and the same holds if we replace in this statement “Chow theoretic” by “cohomological”. In particular, it is not stably rational. We also deduce that the general quartic double solid with seven nodes does not admit a universal codimensioncycle parameterized by its intermediate Jacobian, and even does not admit a parametrization with rationally connected fibers of its Jacobian by a family of-cycles. This finally implies that its third unramified cohomology group is not universally trivial.