The effective cone of the space of parametrized rational curves in a   Grassmannian
  We determine the effective cone of the Quot scheme parametrizing all rank r, degree d quotient sheaves of the trivial bundle of rank n on P^1. More specifically, we explicitly construct two effective divisors which span the effective cone, and we also express their classes in the Picard group in terms of a known basis. 
Shin-Yao Jow
math.AG