MMUSSL
MMUSSL
2014
The theory of algebraic curves is one of the most beautiful corners of algebraic geometry, and it is especially remarkable because of its simplicity and accessibility. Beginning with the study of Riemann surfaces in the mid-nineteenth century, curves continue to be an active are of research today.
After briefly covering some of the basics concepts of algebraic geometry, I’ll talk about the statement and significance of the celebrated Riemann Roch formula for divisors:
l(D) = deg(D)+1-g(C)+l(K_C-D)
and explain some appllications of it, such as to the classification of algebriac curves. In the third lecture, a number of topics might be covered, depending on audience interest. (For instance, using Riemann-Roch to understand symmetries of curves, or understanding the Riemann- Hurwitz formula, which is one of the most powerful tools around for computing the genus of a curve, and hence in applying the Riemann-Roch theorem!)
Prerequisites: Pretty much nothing, but the more you know the less I will lie!
Algebraic Curves
5/19/14