Equations of Hurwitz Schemes in the Infinite Grassmannian
  The main result proved in the paper is the computation of the explicit equations defining the Hurwitz schemes of coverings with punctures as subschemes of the Sato infinite Grassmannian. As an application, we characterize the existence of certain linear series on a smooth curve in terms of soliton equations. 
Jos\'e M. Mu\~noz Porras and Francisco J. Plaza Mart\'in