Fibered stable varieties
  We show that if a stable variety (in the sense of Koll\'ar and Shepherd-Barron) admits a fibration with stable fibers and base, then this fibration structure deforms (uniquely) for all small deformations. During our proof we obtain also a Bogomolov-Sommese type vanishing for vector bundles and reflexive differential $n-1$-forms. 
Zsolt Patakfalvi
math.AG