Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero
Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero
复制标题
小平零维三重积分 Hodge 猜想的失败
DOI：
10.4171/cmh/479
复制
发表时间：
2018
影响因子：
0.9
通讯作者：
J. C. Ottem
中科院分区：
文献类型：
--
作者：
Olivier Benoist;J. C. Ottem
我们证明了一个Enriques曲面和一个亏格至少为1的非常一般的曲线的乘积不满足1-圈的积分Hodge猜想。这提供了第一个例子顺利的射影复杂的三倍的科代拉零维的积分霍奇猜想失败，和第一个例子的非代数扭转上同调类的程度4顺利射影复杂的三倍。
We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first examples of smooth projective complex threefolds of Kodaira dimension zero for which the integral Hodge conjecture fails, and the first examples of non-algebraic torsion cohomology classes of degree 4 on smooth projective complex threefolds.