We compute the Picard group of the moduli stack of genus zero stable quasimaps

to projective space, Grassmannians, and any

flag variety in the case of more than 2

markings. Furthermore, in the case of exactly 2 markings, we calculate the Picard

group of the moduli stack of genus zero stable quasimaps to projective space, Grassmannians,

and to partial

flag varieties where the ranks of the subspaces differ by

more than 1. The first two moduli stacks mentioned are the moduli stacks of stable

quotients, constructed by Alina Marian, Dragos Oprea, and Rahul Pandharipande.

The latter is a generalization of this theory, due to Ionut-Ciocan Fontanine, Bumsig

Kim, and Davesh Maulik. Projectivity of the coarse moduli space is proved first.

The Picard rank is obtained using a torus action on the moduli stack to perform

tangent space calculations. When the number of markings is greater than or equal to 3, generators are

determined by a geometric analysis of the interior of the moduli stack. When the

number of markings is 2, generators and relations are found by intersecting with

curves.