Szego Seminar: Group Law on Curves

Abstract: The group law on an elliptic curve, which allows us to "add" points on an elliptic curve, is well-known and highly celebrated. But what is it

that makes elliptic curves special? Do other curves admit such a group law? I will prove a result about varieties over complex numbers that also have

a group structure where the group operations are given by "polynomial maps". Specializing this to the case of curves, which are one-dimensional

varieties, we will try the answer the above questions  for smooth projective curves over complex numbers.