论文标题
塞伯格（Seiberg）的家族的凯勒（Kähler）表面流畅家庭的不变性
The families Seiberg-Witten invariants of smooth families of Kähler surfaces
论文作者
论文摘要
我们考虑对塞伯格（Seiberg）的不变性对塞伯格（Seiberg）的家庭的不变式的概括，该家族的不变型是一个光滑的4个manifolds家族，纤维差异为4个manifold $ x $。当家庭具有平稳变化的kähler结构时，特别的案例是特殊情况。当$ b_1 = 0 $的某些向量捆绑包的特征类别时，我们将获得不变性的一般计算，这些载体束的特征类别对应于家族的全态线捆绑包。最后，我们将公式应用于Kähler家族的一些示例，可以进行一些进一步的明确计算。我们考虑了一个$ \ mathbb {cp}^2 $的家族，从等级3的第3个复杂矢量捆绑包中获得，一个$ \ mathbb {cp}^1 \ times \ times \ mathbb {cp}^cp {cp}^1 $'s fiber a Kubs a Kuper and kuper a k exive vector vector vector bund bund bunder a k eformal bude bunder a k eformal bunder a Kuld fiber的产物一个被称为普遍爆炸家族的点。
We consider a generalisation of the Seiberg-Witten invariant to the families Seiberg-Witten invariants of a smooth family of 4-manifolds with fibres diffeomorphic to a 4-manifold $X$. Of particular interest is the special case when the family has a smoothly varying Kähler structure. We obtain a general computation of the invariants when $b_1=0$ in terms of characteristic classes of some vector bundles corresponding to the cohomology groups of holomorphic line bundles of the family. Finally, we apply the formula to some examples of Kähler families where some more further explicit computations can be made. We consider a family of $\mathbb{CP}^2$'s obtained from the projectivisation of a rank 3 complex vector bundle, a family of $\mathbb{CP}^1\times\mathbb{CP}^1$'s obtained as the fibre product of the projectivisation of two rank 2 complex vector bundles and a family with fibres being the blowup of a Kähler surface at a point known as the universal blowup family.
