- Registration for Fall term opens Thursday, May 19, 2016.
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This is a first course in algebraic geometry. We will discuss briefly
classical topics including affine and projective varieties. The majority
of the course will be focused on the modern approach to algebraic geometry
via schemes and sheaves. Familiarity with commutative algebra is highly
Some of the results we will discuss are Bezout's theorem, the Nullstellensatz, the group law on an elliptic curve, blowups and birational geometry and Grassmannians.
familiarity with basic category theory as well as commutative algebra; e.g. Atiyah-MacDonald.
OLGA TAUSSKY AND JOHN TODD INSTRUCTOR IN MATHEMATICS
The grade is based entirely on homework.
In certain cases I may grant homework extensions. I highly discourage asking for a homework extension the day before or the day an assignment is due; those requests have a low probability of being granted.
category theory: universal properties, (co)limits. Polynomial rings, algebraic sets and the basic dictionary between algebra and geometry. Results from commutative algebra: various forms of the nullstellensatz, Noether normalization, dimension. Classical algebraic geometry: varieties over an algebraically closed field. Sheaves: defintion, stalks, morphisms of sheaves, global sections, sheafifacation. Schemes: definitions, examples. Topological and sheaf theoretic properties. Morphisms of schemes. Quasicoherent sheaves. Weil and Cartier Divisors, Picard groups.