摘要翻译：
我们证明了对于K3曲面X，Beauville和Voisin引入的Chow环的有限生成子环R(X)在导出的等价条件下是保持的。通过分析球形束的Chern特性证明了这一点。对于定义在数域上的K3曲面X，相关复K3曲面上的所有球丛都定义在$\bar\qq$上，这与Bloch-Beilinson猜想是相容的。除了Beauville和Voisin的工作外，Lazarfeld关于K3曲面中曲线的Brill-Noether理论的结果以及Macri和Stellari在ArXIV:0710.1645中发展的变形理论是讨论的中心。
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英文标题：
《Chow groups of K3 surfaces and spherical objects》
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作者：
Daniel Huybrechts
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  We show that for a K3 surface X the finitely generated subring R(X) of the Chow ring introduced by Beauville and Voisin is preserved under derived equivalences. This is proved by analyzing Chern characters of spherical bundles. As for a K3 surface X defined over a number field all spherical bundles on the associated complex K3 surface are defined over $\bar\QQ$, this is compatible with the Bloch-Beilinson conjecture. Besides the work of Beauville and Voisin, Lazarfeld's result on Brill-Noether theory for curves in K3 surfaces and the deformation theory developed with Macri and Stellari in arXiv:0710.1645 are central for the discussion.
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PDF链接：
https://arxiv.org/pdf/0809.2606