Instructor: Adam S. Sikora
115 Math Bldg
Email: asikora at buffalo dot edu
Class meets: TuTh 11:10-12:25, Math Bldg 122
Prerequisite: Abstract Algebra Course (Familiarity with the notion of a ring, ideal, field). Point set topology.
At the most basic level, Algebraic Geometry studies algebraic sets and algebras of functions on them. More conceptually, it establishes a powerful duality between geometry and commutative algebra, which is central to these and related areas (including number theory and non-commutative geometry). Algebraic Geometry has applications to many branches of mathematics (eg. analysis, combinatorics) and to physics.
Textbook: J. Milne, "Algebraic Geometry", online textbook online.
Supplemental Textbooks: (All of them more elementary than the textbook above, especially the first two.)
Homework: As with all math, it is impossible to learn algebraic geometry in a passive way. For that reason some homework will be assigned, collected and graded.