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

TL;DR

This paper constructs stable omalous bundles on certain surfaces of general type, advancing the understanding of quantum sheaf cohomology's geometric foundations linked to super-string theory.

Contribution

It provides a new method for constructing stable omalous bundles on surfaces of general type, contributing to the geometric aspects of quantum sheaf cohomology.

Findings

Constructed stable omalous bundles on surfaces of general type

Linked quantum sheaf cohomology to geometric bundle constructions

Enhanced understanding of the mathematical structures in super-string theory

Abstract

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.