Spectral Covers, Charged Matter and Bundle Cohomology
  We consider four dimensional heterotic compactifications on smooth elliptic Calabi-Yau threefolds. Using spectral cover techniques, we study bundle cohomology groups corresponding to charged matter multiplets. The analysis shows that in generic situations, the resulting charged matter spectrum is stable under deformations of the vector bundle. 
Duiliu-Emanuel Diaconescu, Gheorghe Ionesei