On the integral Hodge conjecture for real varieties, I
On the integral Hodge conjecture for real varieties, I
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关于实簇的积分 Hodge 猜想，我
DOI：
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发表时间：
2018
影响因子：
3.1
通讯作者：
Olivier Wittenberg
中科院分区：
文献类型：
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作者：
Olivier Benoist;Olivier Wittenberg
给出了实数簇的积分Hodge猜想的一种形式--“实积分Hodge猜想”，并提出了它对Uniruled、Calabi-Yau三重环和有理连通簇的1维循环的有效性问题。我们把它与确定1-圈的Borel-Haefliger圈类映象的问题联系起来，与判定一个没有实点的实簇是否含有偶数几何亏格曲线的问题联系起来，与计算实三重1-圈的Chow群的挠率问题联系起来。关于这些问题，一路上都取得了新的结果。
We formulate the “real integral Hodge conjecture”, a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi–Yau threefolds and on rationally connected varieties. We relate it to the problem of determining the image of the Borel–Haefliger cycle class map for 1-cycles, with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the Chow group of 1-cycles of real threefolds. New results about these problems are obtained along the way.