论文标题
Atiyah课程和变形单数$ g_ {2} - $ instanton的基本障碍
Atiyah classes and the essential obstructions in deforming a singular $G_{2}-$instanton
论文作者
论文摘要
从某种意义上说，当捆绑包的排名为$ \ geq 2 $时，我们发现$ g_ {2} - $ instantons的粘合构造具有$ 1- $ dimensional Singularition的粘合构造的必要障碍。它涉及通过与曲率收缩$ \ mathbb {c}^{3} $中的向量生成的Atiyah类。从直觉上讲，如果在$ 1- $ dimensional单位基因座的组件上的切线连接不是扭曲的fubini-study连接，则胶合不起作用。特别是，如果捆绑包的排名为$ \ geq 3 $，则会失败。
When the rank of the bundle is $\geq 2$, in a certain sense, we found an essential obstruction for the gluing construction of $G_{2}-$instantons with $1-$dimensional singularities. It involves the Atiyah classes generated by contracting a vector in $\mathbb{C}^{3}$ with the curvature. Intuitively speaking, the gluing does not work if the tangent connection at a component of the $1-$dimensional singular locus is not the twisted Fubini-Study connection on a twisted tangent bundle of $\mathbb{P}^{2}$. Particularly, it fails if the rank of the bundle is $\geq 3$.
