Description
Undergraduate Algebraic Geometry introduces algebraic geometry through concrete examples of curves, varieties, and geometric constructions. The book begins with plane conics and cubics, including parametrization, Bézout-type results, the group law on a cubic, and an introduction to the genus of curves. It then develops affine varieties, the Nullstellensatz, functions on varieties, projective varieties, birational equivalence, tangent spaces, nonsingularity, and dimension. The final sections explore applications and connections with topology, differential geometry, commutative algebra, and number theory. With relatively few prerequisites, numerous examples, and exercises, the book provides an accessible starting point for undergraduate students encountering algebraic geometry for the first time.
