Unirational threefolds with no universal codimension cycle

• 成果类型: Article
• 署名作者: Voisin, Claire
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0551-y
• 发表日期: 2015
• 页码: 207-237
• 关键词: abel-jacobi map; vector-bundles; COHOMOLOGY; VARIETIES; families

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.