**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.

**Syllabus**

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.

**Assessment**

Through weekly homework problems, please email your solutions to
tccalggeom@gmail.com