论文标题
submanifold布置补充的合理同副本类型
Rational Homotopy Type of Complements of Submanifold Arrangements
论文作者
论文摘要
我们将提供一个明确的CDGA，控制平滑布置的合理同型类型$ x- \ cup_i z_i $在平滑的紧凑型代数品种$ x $上，超过$ \ mathbb {c} $。这概括了摩根的相应结果，如果分裂的正常交叉处为任意平滑排列。该模型是根据布置$ z_i $给出的，并同意Chen-Lü-Wu用于计算同种学的模型。作为应用程序，我们因Feichtner-Yuzvinksy而尊重形式定理。然后，我们表明，在平滑紧凑型代数品种的色彩构型空间的情况下，Kritz-Totaro模型计算有理同位拷贝类型。
We will provide an explicit cdga controlling the rational homotopy type of the complement to a smooth arrangement $X-\cup_i Z_i$ in a smooth compact algebraic variety $X$ over $\mathbb{C}$. This generalizes the corresponding result of Morgan in case of a divisor with normal crossings to arbitrary smooth arrangements. The model is given in terms of the arrangement $Z_i$ and agrees with a model introduced by Chen-Lü-Wu for computing the cohomology. As an application we reprove a formality theorem due to Feichtner-Yuzvinksy. Then we show that the Kritz-Totaro model computes the rational homotopy type in case of chromatic configuration spaces of smooth compact algebraic varieties.
