Description
Algebraic Geometry: A First Course introduces the fundamental ideas of algebraic geometry through concrete examples and geometric constructions. It develops affine and projective varieties, regular and rational maps, cones, projections, parameter spaces, determinantal varieties, and algebraic groups. The book then examines important properties of varieties, including dimension, degree, smoothness, tangent spaces, tangent cones, and parameter and moduli spaces. Further topics include Hilbert polynomials, Grassmannians, quadrics, and related geometric constructions. Emphasizing classical methods and visual intuition while developing the necessary theory as needed, the book provides an accessible foundation for students beginning advanced study in algebraic geometry.
