A tropical approach to a generalized Hodge conjecture for positive currents
A tropical approach to a generalized Hodge conjecture for positive currents
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正流广义霍奇猜想的热带方法
DOI：
10.1215/00127094-2017-0017
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
June Huh
中科院分区：
文献类型：
--
作者：
Farhad Babaee;June Huh
Demaily证明了Hodge猜想等价于任何（p，p）维有理上同调类的闭流都可以用与子簇相关的积分流的线性组合来近似的陈述，并询问是否任何强正的（p，p）维有理上同调类的闭流都可以用与子簇相关的积分流的正线性组合来近似。使用热带几何，我们构建了一个（p，p）维的电流上的一个光滑的射影品种，不满足后一种说法。
Demailly showed that the Hodge conjecture is equivalent to the statement that any (p,p)-dimensional closed current with rational cohomology class can be approximated by linear combinations of integration currents associated to subvarieties, and asked whether any strongly positive (p,p)-dimensional closed current with rational cohomology class can be approximated by positive linear combinations of integration currents associated to subvarieties. Using tropical geometry, we construct a (p,p)-dimensional current on a smooth projective variety that does not satisfy the latter statement.