Topics in Algebraic Geometry

Tim Dokchitser, TCC, Spring 2015

Lecture times
Thursdays 10-12, 22 January - 12 March
Four extra lectures on deformation theory and models of curves: Wednesdays 1pm-3pm, 22 April - 13 May

Assumed knowledge
I will assume some familiarity with algebraic varieties, and especially with algebraic curves. I will start with a *very* brief review in the first lecture, but basically I will assume that you have seen Zariski topology, regular and rational maps, projective space, non-singular curves, divisors and Riemann-Roch. I will probably manage to stick to varieties throughout the course and avoid scheme-theoretic language completely.

The course will be a mix of two things. One the one hand, I will introduce various basic tools in algebraic geometry - working with families of varieties, flatness, smoothness and properness, functorial approach to varieties, and fine and coarse moduli spaces. One the one hand, I will try to interlace these with examples and applications - I will introduce algebraic groups, abelian varieties, main examples of moduli spaces, and (hopefully) talk about regular and semistable models of curves.

Lecture notes
Informal lecture notes for the main part of the course.

Through weekly homework problems, please email your solutions to