  Quantum sheaf cohomology is a deformation of the cohomology ring of a sheaf.
In recent years, this subject had an impetuous development in connection with
the $(0; 2)$ non-linear sigma model from super-strings theory. The basic piece
in this area is a so-called omalous bundle on the variety we start with. After
a short overview of the subject, we construct stable omalous bundles on some
classes of surfaces of general type.
