Topology of Complex Projective Varieties

Abstract

In this project, I studied some of the interesting results about the topology of complex projective varieties. The project is based on the paper of Klaus Lamotke, titled "The Topology of Complex Projective Varieties After S. Lefschetz." Starting with Lefschetz Pencils, Dual Varieties this thesis covers deep results such as Lefschetz Hyperplane Section theorem, Weak Lefschetz theorem, and Hard Lefschetz Theorem. Along the way, it gives the proof of Lefschetz Hyperplane Section Theorem using Morse Theory, Picard-Lefschetz formula, and Monodromy theorem. Towards the end, we study topology in a neighborhood of a singular point on the complex hypersurfacesIn this project, I studied some of the interesting results about the topology of complex projective varieties. The project is based on the paper of Klaus Lamotke, titled "The Topology of Complex Projective Varieties After S. Lefschetz." Starting with Lefschetz Pencils, Dual Varieties this thesis covers deep results such as Lefschetz Hyperplane Section theorem, Weak Lefschetz theorem, and Hard Lefschetz Theorem. Along the way, it gives the proof of Lefschetz Hyperplane Section Theorem using Morse Theory, Picard-Lefschetz formula, and Monodromy theorem. Towards the end, we study topology in a neighborhood of a singular point on the complex hypersurfacesIn this project, I studied some of the interesting results about the topology of complex projective varieties. The project is based on the paper of Klaus Lamotke, titled "The Topology of Complex Projective Varieties After S. Lefschetz." Starting with Lefschetz Pencils, Dual Varieties this thesis covers deep results such as Lefschetz Hyperplane Section theorem, Weak Lefschetz theorem, and Hard Lefschetz Theorem. Along the way, it gives the proof of Lefschetz Hyperplane Section Theorem using Morse Theory, Picard-Lefschetz formula, and Monodromy theorem. Towards the end, we study topology in a neighborhood of a singular point on the complex hypersurfaces