Quantum Sheaf Cohomology on surfaces of general type I: construction of stable omalous bundles

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.