  Let $C$ be a smooth projective curve of genus 0. Let $B$ be the variety of
complete flags in an $n$-dimensional vector space $V$. Given an $(n-1)$-tuple
$\alpha\in N[I]$ of positive integers one can consider the space $Q_\alpha$ of
algebraic maps of degree $\alpha$ from $C$ to $B$. This space admits some
remarkable compactifications $Q^D_\alpha$ (Quasimaps), $Q^L_\alpha$
(Quasiflags) constructed by Drinfeld and Laumon respectively. In [Kuznetsov] it
was proved that the natural map $\pi: Q^L_\alpha\to Q^D_\alpha$ is a small
resolution of singularities. The aim of the present note is to study the
singular support of the Goresky-MacPherson sheaf $IC_\alpha$ on the Quasimaps'
space $Q^D_\alpha$. Namely, we prove that this singular support $SS(IC_\alpha)$
is irreducible. The proof is based on the factorization property of Quasimaps'
space and on the detailed analysis of Laumon's resolution $\pi: Q^L_\alpha\to
Q^D_\alpha$.
