  We give examples of small data blow-up for a three-component system of
quadratic nonlinear Schr\"odinger equations in one space dimension. Our
construction of the blowing-up solution is based on the Hopf-Cole
transformation, which allows us to reduce the problem to getting suitable
growth estimates for a solution to the transformed system. Amplification in the
reduced system is shown to have a close connection with the mass resonance.
