摘要翻译:
证明了两个光滑射影K3曲面在Fourier-Mukai变换下的一阶变形是等价的当且仅当曲面的全上同调群存在一个特殊的等距,它保持Mukai对、一个无穷小的权-2分解和一个正四维空间的方向。这推广了Torelli定理的导出版本。在此基础上,我们证明了任何Fourier-Mukai函子的Hochschild同调和奇异上同调作用的相容性。
---
英文标题:
《Infinitesimal Derived Torelli Theorem for K3 surfaces》
---
作者:
Emanuele Macri, Paolo Stellari, Sukhendu Mehrotra
---
最新提交年份:
2009
---
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
--
---
英文摘要:
We prove that the first order deformations of two smooth projective K3 surfaces are derived equivalent under a Fourier--Mukai transform if and only if there exists a special isometry of the total cohomology groups of the surfaces which preserves the Mukai pairing, an infinitesimal weight-2 decomposition and the orientation of a positive 4-dimensional space. This generalizes the derived version of the Torelli Theorem. Along the way we show the compatibility of the actions on Hochschild homology and singular cohomology of any Fourier--Mukai functor.
---
PDF链接:
https://arxiv.org/pdf/0804.2552