标题： 同伦变异和高维 Zariski-van Kampen 定理 显示英文标题

标题： Homotopical variations and high-dimensional Zariski-van Kampen theorems

摘要： 1933年，van Kampen描述了复数平面代数曲线补集的基本群。 最近，Chéniot-Libgober证明了这一结果在具有孤立奇点的复射影超曲面补集的高阶同伦群中的类似结论。 他们的描述是通过一些“同伦变分算子”来进行的。 我们在此将“同伦变分”的概念推广到（奇异）拟射影代数簇。 这是进一步推广van Kampen定理的第一步。 在非奇异拟射影代数簇的特殊情况下，提出了一个猜想，并给出了初步的思路。 显示英文摘要

摘要： In 1933, van Kampen described the fundamental groups of the complements of plane complex projective algebraic curves. Recently, Ch\'eniot-Libgober proved an analogue of this result for higher homotopy groups of the complements of complex projective hypersurfaces with isolated singularities. Their description is in terms of some "homotopical variation operators". We generalize here the notion of "homotopical variation" to (singular) quasi-projective varieties. This is a first step for further generalizations of van Kampen's theorem. A conjecture, with a first approach, is stated in the special case of non-singular quasi-projective varieties.