围绕切锥定理
Around the tangent cone theorem
摘要：
上同调跳跃轨迹理论的一个基石是切锥定理，它将空间的特征变量和共振变量的起源联系起来。我们在cdga模型提供的代数背景下，以及在基本群和上同调环提供的拓扑背景下重新讨论这个定理。一般的理论说明了几个类的例子，从几何和拓扑学：光滑的拟射影簇，复杂的超平面安排和他们的Milnor纤维，配置空间，和椭圆形安排。
英文摘要：
A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
