Picard-Lefschetz Monodromy Groups of Quadratic Hypersurfaces

TL;DR

This paper investigates the topological properties and monodromy actions of affine hyperplanes in relation to generic quadratic hypersurfaces in complex space, providing insights into their geometric and algebraic structures.

Contribution

It introduces a detailed analysis of the monodromy groups associated with quadratic hypersurfaces and computes their actions on relevant homology groups.

Findings

Determined the monodromy groups for quadratic hypersurfaces.

Calculated the action of fundamental group on homology groups.

Provided explicit descriptions of the topology of hyperplane arrangements.

Abstract

We study the topology of the space of affine hyperplanes $L \subset \CC^n$ which are in general position with respect to a given generic quadratic hypersurface $A$, and calculate the monodromy action of the fundamental group of this space on the relative homology groups $H_*(\CC^n, A \cup L)$ associated with such hyperplanes.