Generalized Zariski-van Kampen theorem and its application to Grassmannian dual varieties

TL;DR

This paper generalizes the Zariski-van Kampen theorem to broader classes of algebraic varieties and applies it to analyze the fundamental groups of complements of Grassmannian dual varieties, extending classical results.

Contribution

It introduces a generalized Zariski-van Kampen theorem and applies it to fundamental groups of Grassmannian dual varieties, providing new insights into their topological structure.

Findings

Generalized Zariski-van Kampen theorem established

Lefschetz-Zariski-van Kampen type theorem proved for Grassmannian dual varieties

Fundamental groups of complements to Grassmannian dual varieties characterized

Abstract

We formulate and prove a generalization of Zariski-van Kampen theorem on the topological fundamental groups of smooth complex algebraic varieties. As an application, we prove a hyperplane section theorem of Lefschetz-Zariski-van Kampen type for the fundamental groups of the complements to the Grassmannian dual varieties.