Math 625, spring 2015

Algebraic Geometry

Second semester graduate algebraic geometry. This course will focus on algebraic curves and surfaces, especially over an algebraically closed field. Topics on curves will include Riemann-Roch, the Riemann-Hurwitz formula, embeddings in projective space, elliptic curves, Jacobians of curves, and related topics. The study of surfaces will include the adjunction and projection formulas, Riemann-Roch for surfaces, Noether's formula, Hodge Index Theorem, Nakai-Moishezon Criterion, ruled surfaces, monoidal transformations, and related topics. The course will also develop and use cohomology for schemes, both from the Cech and derived functor points of view, a key result being Serre Duality. Other types of cohomology in algebraic geometry will also be discussed.

Class schedule: Mon and Wed, 1:30-3pm in DRL 4N30, from Jan. 14 to April 29, 2015, and some occasional meetings on Fridays at the same time and place (as announced). Note: Due to holidays and student conflicts, there are no classes on January 19 and from March 9-18. Classes will be held on the following Fridays: Feb. 27, March 6, March 20, April 17, April 24.

Main references:

Homework assignments for Math 625