The effective cone of the space of parametrized rational curves in a Grassmannian

Abstract

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 $${\mathbb{P}^1}$$ . 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.