Seminar in Real and Complex Geometry

Thursday, June 6, 2019, 16:00-17:00, Schreiber building, room 209

Madeline Brandt (Berkeley)

Symmetric powers of algebraic and tropical curves


Recently, tropical geometry has emerged as a tool for studying classical moduli spaces by associating to every variety a polyhedral complex which comes as its non-Archimedean skeleton. Classically, it is known that the d-th symmetric power of a smooth, projective algebraic curve X is again a smooth, projective algebraic variety which functions as the moduli space of effective divisors of degree d on X. In this talk, I will discuss two ways to tropicalize this statement. The first way is to take the d-th symmetric power of the tropicalization of X, and the second is to tropicalize the d-th symmetric power of X itself. In recent work with Martin Ulirsch, we show that in fact the two agree. I will present all necessary definitions for understanding the above statement and I will sketch the proof.