K3 曲面的导出等价与定向
代数几何
2019-12-19 v4 范畴论
摘要
两个 K3 曲面导出范畴之间的任何 Fourier--Mukai 等价都会诱导其上同调的 Hodge 等距，这些上同调被视为赋予 Mukai 配对的权为二的 Hodge 结构。我们证明了该 Hodge 等距保持了四个正方向的自然定向。这导致了对所有自等价群在上同调上作用的完整描述，非常类似于确定由自同构诱导的所有 Hodge 等距的 K3 曲面经典 Torelli 定理。
引用
@article{arxiv.0710.1645,
title = {Derived equivalences of K3 surfaces and orientation},
author = {Daniel Huybrechts and Emanuele Macri and Paolo Stellari},
journal= {arXiv preprint arXiv:0710.1645},
year = {2019}
}
备注
This version only contains the proof that every equivalence between the derived categories of two K3 surfaces induces an orientation preserving Hodge isometry. The more formal aspects of our proof contained in the first sections of arXiv:0710.1645v2 appear now in the independent paper arXiv:0809.3201. 29 pages. Final version to appear in Duke Math. J