Towards a Tropical Proof of the Gieseker-Petri Theorem
  We use tropical techniques to prove a case of the Gieseker-Petri Theorem. Specifically, we show that the general curve of arbitrary genus does not admit a Gieseker-Petri special pencil. 
Vyassa Baratham, David Jensen, Cristina Mata, Dat Nguyen, Shalin   Parekh
math.AG