Free online courseAlgebraic geometry

Course Description

Explore the fascinating world of Algebraic Geometry with VisualMath's comprehensive online course designed for beginners and enthusiasts. This in-depth course delves into fundamental concepts such as algebraic varieties, conic sections, ideals of sets, and the foundational principle of Hilbert’s Nullstellensatz. Gain insight into the coordinate ring and understand the significance of the Zariski topology in algebra. Learn about the dimension of a variety and how regular functions play a role with the identity theorem and examples provided for clarity.

Advance your understanding with thematic explorations of sheaves across multiple takes, alongside ringed spaces and their relevance. Discover the essence of prevarieties, abstract varieties, and projective space, including projective varieties and the projective Nullstellensatz. Traverse the concepts of projective closures, Segre and Veronese embeddings, and delve into the intriguing realms of Grassmanians, with a focus on Plücker coordinates and Schubert calculus.

Develop your skills by examining birational maps, the process of a blow-up, and understanding tangent cones and smooth varieties. Study the Jacobi criterion, dual curves, and the mystery of the 27 lines. Schemes are explored in much detail across multiple sessions, covering regular functions, morphism of schemes, sheaves of modules, tautological sheaves, skyscraper sheaves, and the process of sheafification.

Gain a robust insight into quasi-coherent sheaves, Kähler differentials, and the complexities of sheaf cohomology. Finally, venture into the emerging field of tropical geometry with this meticulously crafted course that aims to lay a strong foundational understanding while intriguing the mind with abstract and applied aspects of algebraic geometry.