论文标题
关于某些非脱位四边形的工会的同源
On the Homology of Unions of Certain Non-Degenerate Quadrics in General Position
论文作者
论文摘要
在扰动量子场理论的复杂分析中引起的问题的促进，我们研究了某些综合维度$ n $一般位置的某些非偏移二次偏移膨胀的有限工会的同源性。此类工会的同源性和$ \ mathbb {c}^{n+1} $相对于此类工会的同源性被分解为这些超曲面各种可能相交的同源组的直接总和。这使我们能够计算出同构的同源组。此外，我们通过构建相关联合的足够大的CW-Subclex来计算这些超曲面的特定布置的明确集合。所有发电机与$（i \ cdot \ mathbb {r}）^{n+1} $的borel-moore同源类别的交点索引计算。
Motivated by problems arising in the complex analysis of perturbative quantum field theory, we investigate the homology of finite unions of certain non-degenerate quadratic affine hypersurfaces of complex dimension $n$ in general position. The homology of such unions and the homology of $\mathbb{C}^{n+1}$ relative to such unions is decomposed into a direct sum of homology groups of the various possible intersections of these hypersurfaces. This allows us to compute the homology groups up to isomorphism. Furthermore, we compute an explicit set of generators for a specific arrangement of these hypersurfaces by constructing a sufficiently large CW-subcomplex of the union in question. The intersection indices of all generators with the Borel-Moore homology class of $(i\cdot\mathbb{R})^{n+1}$ in the complement of the union of surfaces are computed.
