  Uniform large deviations for the laws of the paths of the solutions of the
stochastic nonlinear Schrodinger equation when the noise converges to zero are
presented. The noise is a real multiplicative Gaussian noise. It is white in
time and colored in space. The path space considered allows blow-up and is
endowed with a topology analogue to a projective limit topology. Thus a large
variety of large deviation principle may be deduced by contraction. As a
consequence, asymptotics of the tails of the law of the blow-up time when the
noise converges to zero are obtained.
