  We look at the following question raised by Koll\'ar and Peskine. (Actually,
it is a slightly weaker version of their question.)
  Let $V_t$ be a family of rank two vector bundles on $\Bbb P^3$. Assume that
the general member of the family is a trivial vector bundle. Then, is the
special member $V_0$ also a trivial vector bundle?
  We show that this question is equivalent to the nonexistence of morphisms
from $\Bbb P^3\to \mathcal{X}$, where $\mathcal{X}$ is the infinite
Grassmannian associated to SL(2). We further reduce this question to the
nonexistence of $\Bbb C^*$-equivariant morphisms from $\Bbb C^3\setminus \{0\}
\to \mathcal{M}_d$ (for any $d>0$), where $\mathcal{M}_d$ is the Donaldson
moduli space of isomorphism classes of rank two vector bundles $\mathcal{V}$
over $\Bbb P^2$ with trivial determinant and with second Chern class $d$
together with a trivialization of $\mathcal{V}_{|\Bbb P^1}$.
