Linked symplectic forms and limit linear series in rank 2 with special   determinant
  We generalize the prior linked symplectic Grassmannian construction, applying it to to prove smoothing results for rank-2 limit linear series with fixed special determinant on chains of curves. We apply this general machinery to prove new results on nonemptiness and dimension of rank-2 Brill-Noether loci in a range of degrees. 
Brian Osserman and Montserrat Teixidor i Bigas
math.AG