Complements to ample divisors and Singularities

TL;DR

This paper reviews recent advances in Alexander invariants of quasi-projective manifolds, focusing on singularity theory methods and extending topological results to new classes of algebraic curves and hypersurfaces.

Contribution

It introduces new topological results for complements of singular curves on simply connected smooth projective surfaces, expanding the scope of previous invariants.

Findings

Extended Alexander invariants to curves on smooth projective surfaces

Established new topological properties of hypersurface complements

Connected singularity theory with algebraic topology of complements

Abstract

The paper reviews recent developments in the study of Alexander invariants of quasi-projective manifolds using methods of singularity theory. Several results in topology of the complements to singular plane curves and hypersurfaces in projective space extended to the case of curves on simply connected smooth projective surfaces.