Instructor: Adam S. Sikora 115 Math Bldg
Email: asikora at buffalo dot edu
Class meets: TuTh 11:00-12:20, Math Bldg 250
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 (for example number theory, arithmetic geometry, and non-commutative geometry). Algebraic Geometry has applications to other branches of mathematics (eg. analysis, combinatorics) and to physics.

Textbook: Will be decided in the first week of classes based on interests and preferences of students.

Supplemental Textbooks: (All of them more elementary than the textbook above, especially the first two.)

• J. Milne, "Algebraic Geometry", online textbook online.
• "An Invitation to Algebraic Geometry" by Smith, Kahanpaa, Kekalainen and Traves.
• Cox, Little, and O'Shea, "Ideal, varieties and algorithms"
• I. Shafarevich, "Basic Algebraic Geometry I"

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.