Rational Homotopy Type of Complements of Submanifold Arrangements

We will provide an explicit cdga controlling the rational homotopy type of the complement to a smooth arrangement X-∪_i Z_i in a smooth compact algebraic variety X over 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.