The Picard Group of the Moduli Space of Genus Zero Stable Quotients to Flag Varieties
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