科研之友
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摘要
We prove that the general quartic double solid with nodes does not admit a Chow theoretic decomposition of the diagonal, (or equivalently has a nontrivial universal group,) 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 codimension cycle 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.
- 出版日期2015-7
