Spin (7)-instantons, stable bundles and the Bogomolov inequality for complex 4-tori
Spin (7)-instantons, stable bundles and the Bogomolov inequality for complex 4-tori
复制标题
自旋 (7)-瞬时、稳定丛和复数 4 环面的 Bogomolov 不等式
DOI：
10.1016/j.matpur.2013.11.004
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
V. Muñoz
中科院分区：
文献类型：
--
作者：
V. Muñoz
使用 8 维自旋 (7) 流形的规范理论，我们开发了一种称为自旋旋转的过程，它将 4 维复环上的向量束上的（稳定）全纯结构转换为不同复环上的新全纯结构。我们通过将可分解的韦伊阿贝尔簇旋转为不可分解的簇来展示这一过程的重要示例。作为副产品，我们获得了 Bogomolov 型不等式，它对 4 维阿贝尔簇上稳定丛的存在给出了限制，并给出了比通常的 Bogomolov 不等式更强的例子。
Using gauge theory for Spin (7) manifolds of dimension 8, we develop a procedure, called Spin-rotation, which transforms a (stable) holomorphic structure on a vector bundle over a complex torus of dimension 4 into a new holomorphic structure over a different complex torus. We show non-trivial examples of this procedure by rotating a decomposable Weil abelian variety into a non-decomposable one. As a byproduct, we obtain a Bogomolov type inequality, which gives restrictions for the existence of stable bundles on an abelian variety of dimension 4, and show examples in which this is stronger than the usual Bogomolov inequality.