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摘要翻译：
两个K3曲面的派生范畴之间的每一个Fourier-Mukai等价都导致它们的上同调的Hodge等距，将其看作赋有Mukai配对的权重为2的Hodge结构。我们证明了这个Hodge等距保持了四个正方向的自然定向。这就得到了关于所有自等价群在上同调上的作用的完整描述，非常类似于K3曲面的经典Torelli定理，它决定了所有由自同构引起的Hodge等距。
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英文标题：
《Derived equivalences of K3 surfaces and orientation》
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作者：
Daniel Huybrechts, Emanuele Macri, Paolo Stellari
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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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一级分类：Mathematics 数学
二级分类：Category Theory 范畴理论
分类描述：Enriched categories, topoi, abelian categories, monoidal categories, homological algebra
丰富范畴，topoi，abelian范畴，monoidal范畴，同调代数
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英文摘要：
Every Fourier--Mukai equivalence between the derived categories of two K3 surfaces induces a Hodge isometry of their cohomologies viewed as Hodge structures of weight two endowed with the Mukai pairing. We prove that this Hodge isometry preserves the natural orientation of the four positive directions. This leads to a complete description of the action of the group of all autoequivalences on cohomology very much like the classical Torelli theorem for K3 surfaces determining all Hodge isometries that are induced by automorphisms.
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PDF链接：
https://arxiv.org/pdf/0710.1645
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