The integral Hodge conjecture for two-dimensional Calabi–Yau categories
The integral Hodge conjecture for two-dimensional Calabi–Yau categories
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二维Calabi-Yau范畴的积分Hodge猜想
DOI：
10.1112/s0010437x22007266
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发表时间：
2020-04
影响因子：
1.8
通讯作者：
Alexander Perry
中科院分区：
文献类型：
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作者：
Alexander Perry
我们建立了范畴的积分Hodge猜想的一种形式，证明了适当变形等价于K3或交换曲面的派生范畴的二维Calabi-Yau范畴的猜想，并用它推导了通常的簇积分Hodge猜想的情形。在此过程中，我们证明了二维Calabi-Yau类型族的变分积分Hodge猜想的一个形式，以及这类类型族中对象的相对模空间的一个一般光滑性结果。我们的机器也适用于中间雅可比的结构，例如，根据派生范畴的准则，当它们作为曲线的雅可比之和拆分时。
We formulate a version of the integral Hodge conjecture for categories, prove the conjecture for two-dimensional Calabi–Yau categories which are suitably deformation equivalent to the derived category of a K3 or abelian surface, and use this to deduce cases of the usual integral Hodge conjecture for varieties. Along the way, we prove a version of the variational integral Hodge conjecture for families of two-dimensional Calabi–Yau categories, as well as a general smoothness result for relative moduli spaces of objects in such families. Our machinery also has applications to the structure of intermediate Jacobians, such as a criterion in terms of derived categories for when they split as a sum of Jacobians of curves.